I am experiencing the same issue, on both 127 and 128 (the 32 bit UI versions, downloaded from http://mameui.classicgaming.gamespy.com/.
I retried 126, and the cheats are still there. When you say "Uninstall", how did you do it - just delete the MAMEUI32.exe, or also go into the registry to delete keys? I tried just deleting the .exe and reinstalling, but had the same problem.
When using 127 or 128, I confirmed that the "Options", "Directories...", "cheats" directory is the location where the cheat.zip is located. However, when I select "Options", "Cheat file...", no window pops up to select the location - unlike when I select "history file..." or "info file...".
Any help/assistance would be appreciated...