My first thought is...

Windows 8.1 may have included some new display drivers that are not fully compatible with Firefox. To address that, we usually recommend disabling hardware graphics acceleration in Firefox and in Flash:

(A) In Firefox, un-check the box here and restart:

orange Firefox button (or Tools menu) > Options > Advanced > General > "Use hardware acceleration when available"

(B) In Flash, see this support article from Adobe: http://helpx.adobe.com/flash-player/kb/video-playback-issues.html#main_Solve_video_playback_issues

However, it may also help to visit your computer manufacturer's website for updated graphics drivers or, if you installed a third party product after you got your PC, that manufacturer's website.

If the first thought didn't help...

When the Flash plugin crashes, Firefox usually records information about what was happening at that moment. You can submit that data to Mozilla and share it with forum volunteers to see whether it points to the solution. Please check the support article "Firefox Crashes" (especially the last section) for steps to get those crash IDs, and then post some of the recent ones here.