Hey Hazem, ''Slip'', in the context above, means the same as ''to make a mistake or error'' / ''to fail to do something''. As a matter of fact, the phrasal verb ''slip up'' is the correct idiom used to convey this meaning. However, most people choose to say only 'slip' in place of 'slip up'. Here are some other examples that may help you: E.g.: ''I think your brother slipped (up) on compiling this list - there are a lot of names missing!'' E.g.: ''I slipped (up) when I said my plane would arrive at 6:00 am — I meant 6:00 pm.'' E.g.: ''She slipped (up) when she delivered those invitations to the wrong people.'' Hope that helps!!!

Slip, in this context, means "to mess up" or "fail".

The use of English in this text is not very good: I hope the language the book teaches you is better than this. You are correct in thinking that it means 'become less': particularly when talking about effort, quality or progress. Slipping here means failing to make progress, or even going backwards - as if you slipped downhill while trying to climb up. It is saying that you are the only person who can fix it if you fall behind with your learning. To slip does not generally mean 'make a mistake', we typically use the phrasal verb 'slip up' for this, as described by Luiz, but it is not used here because this is not what they mean.

It would be extremely rare for a native British speaker, to say you slipped. They would always instinctively and naturally use the full idiom or phrasal verb "slipped up". Second language learners of English are likely to say slipped and natives may make the mental correction in their mind and not point out the different use of "to slip"