I can 100% guarantee you that getting a static IP will not fix the problem.
However, if you do feel so inclined and wish to waste bucketloads of money, you can shell out some extra for a static IP from your ISP.
With comcast, for example, their plans require a business service plan to get a static IP, so you end up having to pay something like $100/mo (you also get an incredible connection, but that's beside the point).