〜わけにはいかない means "cannot afford to" or "must not" — there are reasons (social obligation, circumstances, morals) preventing you from doing X.
Social/moral constraint - Can''t do X because it would be wrong
Circumstances - Situation doesn''t allow for X
I promised, so I have to go. (lit: can''t not go)
ないわけにはいかない (double negative) = must do, have no choice but to
Dictionary form + わけにはいかない = cannot do
ない form + わけにはいかない = must do (double negative)
Variant without は: わけにいかない
I can't afford to give up here.
It's work, so I can't take a day off.
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