Is there a journal for replications in experimental economics? Is there a journal that publishes replications (failed and successful) of (published) experiments? And, if not, why not?
And what about failed experiments (i.e. experiments with insignificant results)?

I think replications of experiments are very important, as experiments in economics depend on many different things and most of them we don't really understand. Having replicated an experiment helps to make sure that the results obtained are not by pure chance (or worse). And, more importantly, failed attempts to replicate a study shows that there was something wrong in one of the studies.

As this was not clear: I am talking about lab experiments, not field experiments.
Experimental Economics states: "The journal will also consider
articles with a primary focus on methodology or replication of
controversial findings."
The Economics e-Journal takes replications from any field.


The Behavioral Economics Replication Project could be interesting for you. They presented their research at the 2016 American Economic Association Annual Meeting.