I have never had any problem with Sigil with WinAmp (nor indeed between Sigil with anything else). That on both 32 bit and 64 bit machines, but all now are Windows 8, however I would be surprised if running Win 8 as opposed to Win 7 was the key to no problem.
WinAmp is prone to issues, a common one being it leaving background processes running when closed (which can prevent WinAmp running again unless they are manually closed or the PC restarted). But I have tested to confirm that does not cause Sigil an issue on both 32 and 64 bit machines. Another is some of its plugins are claimed to be problematic, but I personally have not had any issue, however I only run one non standard plugin in WinAmp. But those are only known, as far as I am aware, with causing issues within WinAmp itself.
Until others come up with the same issue of WinAmp vs Sigil as being common and then proven, I would not tend to rush around in circles blaming the applications (nor their developers for lack of concern as has ben inferred
) but rather look to issues of my own in my own local environment.