I'm just curious how other storyguides rule on the duration of arcane connections. If something lasts for days how many days? Obviously I could create a house rule (each interval that passes whether it be day, week, or whatever could incur a check for expiry), but I wondered if anything more solid is covered anywhere.
It most likely depends on the nature of the connection and what the object is, but perhaps three-five days is about right. Arcane Connections aren't an exact science, afterall. 
Days are less than weeks. So, two to thirteen.
It all depends on factors such as natural affinity to the target, contaminating contacts afterwards, natural degradation of the physical medium, etc.
So let's say if you retrieve an item of clothing that your target wears often, right after it has been worn for a day. You are careful to avoid touching it with your bare hands and store it inside a container that prevents it from coming into contact with someone else. Under those conditions the arcane connection may very well last for a week or even a bit more.
If, on the other hand, you just grab a piece of clothing that he just wore but usually doesn't use that much, stuff it into your bag and go out into pouring rain. The arcane conneciton may very well last only for a single day.
I usually roll a simple die, so the rock gathered on an expedition will work to allow Leap of Homecoming for 1-10 years. It's a house rule that has served my group well.
We have used a similar houserule on occasion.