I will share an experience I had recently. The problem most likely has nothing to do with Tiny Core, but I will share just in case.
I use a hard drive with several partitions. Each time there is a new version of Tiny Core I install it on a different partition to the previous one. If it does not work properly, I can still use the previous one. This has come in handy in the past, as I have sometimes experimented with making modifications to Tiny Core, and in some cases my modifications have not worked. I use Tiny Core on the other partition to fix it.
I recently installed Tiny Core 3.2. It worked properly.
I then installed Tiny Core 3.3rc2 on another partition.
It booted very slowly. I decided to time it, to be sure, and to see how much slower. The first time I timed it, it was one minute slower. The next time, it was much slower again, and there were some error messages - they did not stay there long enough for me to read. I figured it was some sort of corruption on the hard drive. I booted into Tiny Core 3.2, and it was slower now. I copied all of my personal files to another hard drive.
I decided to repartition the hard drive using Parted Magic, and reinstall on the repartitioned hard drive. Parted Magic was not able to repartition the hard drive. The hard drive must be failing.
I put another hard drive in the computer, partitioned it using Parted Magic, and reinstalled Tiny Core. I am now running Tiny Core 3.3rc2, with no problems.
It seems that the problem was hard drive failure. When I have time, I want to put the faulty hard drive in another computer and try to partition it. Just in case.
I am mentioning this, just in case there is something corrupting the hard drive. It might be incompatible extensions. I am running the same extensions now, with no problems, so this is unlikely.