When Firefox crashes, it 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.

If Firefox won't stay up long enough to do that, the article mentions an alternate (more difficult) way to extract the IDs.

Also consider:

• Uninstall BitGuard to fix crashes with Firefox
• Troubleshoot Firefox issues caused by malware