Static IP shouldn't make any difference when you're on the receiving end. If it's a connection problem on your end instead of the sender's end, then yes, there is a good chance it's related to your ISP. However, that may just mean that you have bad cables leading to your house and trying to get your ISP to fix something like that or even to diagnose it enough to know if that's the problem is not going to be easy or cheap.
You can try having other people send files to you to test it. If others can send to you without a problem, then it's most likely that sender who has the problem. If the problem happens no matter who sends to you, then it's likely on your end somewhere (including possibly your ISP).