The level in question from Lemmings United also shows as being last edited with V1.25, which I believe also had bugs around this (in that it incorrectly used a deprecated keyword instead of the current one). Running the level through Cleanse, or open -> manual correct -> save, will fix it.
As all examples have related to either a known-and-fixed bug in experimental builds, or to outdated-format levels that had not been cleansed, it looks like there's no actual issue with the current stable editor here.
If anyone encounters this issue again, please:
1. Check the level in-game. If the skill count is missing there too, it's lost from the level data altogether, and will need to be fixed manually.
2. If it's fine in-game, run the level through Cleanse Levels (on the title screen of a pack containing it, press F8).
3. Open the level in the stable version of the editor, V1.27 or higher (Help -> About to check which version you have). Only if the skill count is still wrong in the editor (or when saving again from the editor now), report it.
Please also make sure - in general - that your copy (or copies, if you have more than one) of the editor are up-to-date, unless it's an old version you're intentionally keeping and clearly know that it's an old one. At the time of this post, the latest stable version is V1.27.