Based on what I read in past threads, any time Firefox crashes (doesn't close properly), the cache starts from scratch. This is because the indexes may be damaged and using them may result in displaying gibberish. I am not aware of a way around that, but for power cuts, consider buying a UPS (uninterruptible power supply) to protect your computer.

Many UPS units come with a cable to plug into the computer. Then during a blackout, and the UPS is running out of energy, a program in the computer is triggered, making the computer do a full shut down.

Not only due to power-cut, also sometimes when Firefox is not responding and End process, This happens again.

I do not know of any way to prevent Firefox from invalidating your existing cache when recovering from a crash. Maybe there's a way to fool Firefox into thinking it did not crash? But I don't know how to do that.

Regarding the problem of Firefox Not Responding, can you spot any pattern to when that happens?

If I may point out, the reason the cache is cleared is because it is considered corrupt by Firefox. Question, do you really want your computer running with corrupted files?

As to Firefox is not responding, did it crash, just close, or what?

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We're sorry to hear that Firefox is crashing. In order to assist you better, please follow the steps below to provide us crash IDs to help us learn more about your crash.

1. Enter about:crashes in the Firefox address bar and press Enter. A Submitted Crash Reports list will appear, similar to the one shown below.
2. Copy the 5 most recent Report IDs that start with bp- and then go back to your forum question and paste that into the "Post a Reply" box.

Thank you for your help!

More information and further troubleshooting steps can be found in the Troubleshoot Firefox crashes (closing or quitting unexpectedly) article.