I will give it up to a couple weeks and I will always follow up asking if there is any interest. If no response, then I will remove.
I know that I need to get better at responding to offers as well which is why I think the asking if there is any interest is a key. Sometimes my time is limited for a given week and trades come and go before I look at them in detail. This is the point where I need to get better and say I have an interest but give me a few days.
I also get frustrated with offers or counter offers that just don't make sense, especially base commons from common sets for inserts or tough regional cards. Sometimes it is neither party knows the value of the others cards which is fine. For those trades it takes more time to figure something out and I might not have the time to dedicate and then they disappear.
Probably this is a tangent into other topics, so back on topic: a couple weeks with follow-up.