Greg has given a couple of good answers, but I think they are only used in some regions. In the US, the phrase "to go limp" is never used to mean "to lose interest." The only metaphorical meaning I'm familiar with is sexual (referring to a man "going limp").

The most common non-literal meaning is 'lose interest'. To go limp on something is to lost interest on something. You had a lot of interest or motivation, then suddenly you lose all this interest to continue - you go limp on it. Always there's the idea you previously had a strong interest on doing something. But that interest suddenly sags, goes limp and you're left with no enthusiasm for continuing. "I really wanted to go overseas last year, but I went limp on the idea and gave it up"