Healing is either "instant" (permanent if a ritual) OR a bonus on he recovery roll. I have a player who wants to reduce healing time (e.g from 1 week to 2 days for Light Wounds). The player describes this as concentrating the body's resources. I cannot see why this would not be possible - if CrCo can do it instantly then it should be able to do it over 2 days and without requiring him to research a breakthrough.
My question is, should speeded up healing use Vis?
Hmm, I'd say yes.
I don't see the rules as written allowing for this. I would nevertheless treat it as simply permanent healing that takes time to manifest, so would make it a Ritual spell but non-momentary in duration. It would be more expensive than using a Momentary spell to heal, but hey - if he wants to heal more cheaply, that's a Breakthrough.
If you take into account the fact that it might take several rolls (i.e. several weeks/months/seasons) to recover from a wound, getting a recovery bonus is already "speeding up" the healing process by "concentrating the body's resources".
If the player insists on accelerated recovery and you feel like granting that request, you could ask for an immediate aging roll modified by the wound penalty, without the benefit of eventual longevity potions. The energy has to come from somewhere, doesn't it? And the character remains weakened (e.g. stuck at Weary) for the remainder of the normal recovery period.
But personally, I wouldn't grant it. It changes the flavour of the game by attempting to bypass a built-in limitation.
The reason healing in Ars Magica is so 'difficult' is purely a mechanical choice. The authors of the game wanted to cap the powers of magi. One of the distinct differences between Ars Magica and variety of other fantasy games is that while the powers of Hermetic Magi are vast, they are not capable all of things.
"In" game these caps have been detailed as the Essential Limits. But the Essential Limits exist to define the mechanical extremes of the game. The authors felt that if these mechanic limits were not in place then anything would be possible for a Hermetic Magus and there would be no way to maintain a credible gaming world.
It's your game, feel free to do what you will. Most of us here discuss by the book interpretations or minor tweaks to the game. I think an ageing roll to make healing even faster is a fair tweak.
I think you need to consider why the authors made healing as slow as it is. Consider that most games occur in a saga atmosphere where a lot of time can pass. Consider that the core game encourages role playing over roll playing. These things, combined with the fact that dead=dead make combat a serious matter to consider before entering it. "Slow" healing supports this postion.
If you wish to tweak the game and play a more episodic game, where vast amounts of time are not as important as 'the hear now'. Then fast healing may suit you. However consider that fast healing will likely increase the amount of combat in the game as the reprocussions of combat are no longer as pronounced.
That is if you take a massive beat down and spell can make you better, then so what? What's a beat down? Also consider that any spell can be replicated as a potion. Now it's possible for say every grog or at least companion to carry two or three 'healing potions' on them. Such an action starts to turn Ars into another game I won't mention here. That may be what you want. If so, pursue that. However before you pursue that option, simply consider how your game will change if people heal quickly.
As a side note. In my first Ars Magica game oh so many years ago I had the troupe fight a Drake detailed in "The Dark Ages" adventure. The Drake killed most of the troupe and the ones that survived took months to heal. I clearly remember us after the session exclaiming, "It's like 6 weeks for this guy to get better!" "This guy took 3 months!" We were all saying "OH MY GOD!"
The SECOND session no one wanted to get into a fight. Eventually the guy that took 3 months to heal fought a demon. It took him ANOTHER 3 months to hea! After that second fight we were done with arbitrary combat and our abilities as ROLEplayers immediately improved. Now we tell stories and when combat comes up, it's a serious matter with serious consequences. Ars Magica is directly responsible for turning me from a hack and slash player into a storyteller. Slow healing is apart of that of that process. Thank you slow healing, thank you. 
Thanks for all these thoughts.
YR7 - hell like the suggestion that this slower healing will be harder than the instant version - not!
FRUNY - We'd already noted that magic can be used effectively to near guarantee the fastest possible natural healing - a level 15 CrCo gives +15 on recovery (base +1 touch). Within the game world I am not sure that the player concerned's explanation that the body's defences are being concentrated does not leave it open to exactly the sort of problem you propose - aging or similar.
TUURA - I agree with what you write. Don' fight unless you have to (and my game is not combat heavy). I am not sure even why he thinks this spell is necessary.
I currently plan to allow a spell to halve the periods between recovery rolls. However there will be a slightly higher chance of problems (-2 to die roll). No Vis will be required. It can only be applied to one wound at a time. Base Level 10.
Incidentally, there has been some discussion of that same topic before.
A -2 wouldn't stop them from also casting a spell giving a recovery roll bonus, unless you specifically rule them incompatible.
If they want fast healing, they should pay for it. In vis or otherwise. Otherwise you'd think it would be the preferred healing method in the Order already.
Plus if you can make the body recover from wounds more quickly, it should be possible to make it recover from fatigue more quickly, too, no? There goes the Limit of Energy.
Hmm... make the accelerated recovey painful (a season's worth of pain in one week!) and thus have psychological side effects (lower Brave and Loyal scores)? Have it give one Aging Point, without a roll? Make a 6+ Stamina check or gain one Decrepitude? 
Warping is always fun, too. You can make the target more susceptible to bad air, humor imbalances, disease spirits and other demons: while the body is busy fighting the designated wound, its defenses are down on the other fronts.
And the recovery of the other wounds is suspended? Or you do have to check whether they worsen (cannot improve).
Guaranteed vis-less fast recovery means that if a mage ever gets wounded, he can recover without his season's work being affected, and not have to pay for it. Non-ritual fast recovery means (as Tuura pointed out) that you can the effect in a magic item. It means that if your shield grog get slapped down in the middle of a story, you can bring him back up without delay. It means you don't have to reach for the higher-level instant-healing spells either (avoids warping, don't need overly high CrCo totals).
Heck, just ask him.
I agree with all of Fruny's points, but this especially. It looks like your player wants a free pass. If he wants this extremely useful ability ("fast healing"), he should pay for it - preferably in story. I wouldn't mind coming up with some mystery cult along those lines for example - perhaps if he'll join the secret cabal of Isis worshippers, where fast healing is but a stepping stone in the path to learn Isis's greaterst mystery, the secret of restoring the dead "Osiris" to life.
Heh. Fast healing comes in handy when you're due for the "being chopped up in little bits and then mummified" ordeal. 
Ok ok, I like where this is going. One question:
Do you cast this spell before or after your brains are scraped out of your head through your nose?