Deleting all of the breakpoints solves the problem when I hit this error. Disabling the breakpoints was not enough – they had to be deleted.
I was able to attach to a process numerous times. Once I added a conditional breakpoint (with a few checks), I started getting this error when attempting to attach to that same process.
The error provided in the question is one problem. I also received an error stating that a debugger was already attached when I tried again. Either way, deleting breakpoints solved it.