訳(わけ)には行(い)かないCannot afford to, No way, Impossible to do

わけにはいかない is a statement that combines わけ 'to be so', 'reason', or 'cause', with the case marking particle に, the adverbial particle は, and the 'cannot go' meaning of 行(い)かない. It can be translated as 'cannot afford to (A)', or 'impossible to (A)'. However, the literal meaning is much closer to 'it cannot be so that (A)'.

This structure will be used directly after the non-past form of verbs, in order to highlight them as being either highly undesirable, or highly unattainable.

Although わけにはいかない primarily highlights things that are undesirable, it may also highlight something that is desirable, but impossible for some reason. This will depend largely on the speaker's tone of voice, and context of the conversation.

In these types of sentences, the expression is quite similar to the 'I guess it's just not meant to be so' nuance that can be conveyed in English, highlighting regret.