How much physical memory is on the server, how much memory is used during those peak times, and how much memory did the vendor set for fixed allocation?

If I had to take a guess, it sounds like there may not be that much physical memory on the server. During peak times, the Windows Server would take time allocation more virtual memory. It's also possible that SQL Server wasn't caching as much.

You could get the same effect by leaving it with dynamic allocation but setting a minimum.