How do the words in 让我不断想不敢再忘记你 piece together (from the song Mouse Loves Rice, 老鼠爱大米)?
Maybe you could break them down like such to get a better understanding:


  让我不断想, 不敢再忘记你


In the first clause, “不斷” is an adverb, meaning "continuously; without stopping", that applies to “想”. That leaves us a meaning of "continuously thinking (of you)".

In the second clause, you forgot to include “不敢” here, so the meaning should be "not dare to forget you again".