As per my experience, I don't have trouble keeping my modem open all the time. You'll just have to reset (off and on the power) if you cannot connect and feel that it hanged (and this seldom happens, maybe once in 2 months). And Yes QaQc is right, place it in a cool place. Some friends even used to buy a small/portable fan to keep it cool, but i don't think it is necessary.

You can keep it open all the time to save you the trouble of waiting for connection every time you need it.

Ohh, and keep it secured so nobody can steal or access your signal, it is probably one of the cause of frequent hanging if too many users are connected to your network (free) and down loading large amount of bytes.

Goodluck!