Hi @Sara_
Trying to understand your issue better,
What version of desktop are you working with?
Is your mask a raster or feature area?
Perhaps you are able to share you model and data with me and I can try to reproduce on my end? (attach to this thread?)
Suggested to try and troubleshoot.
1) Run extractbymask stand alone (the case that works for you). Create a new model and drag the result from GP Result window into the model. Does this work? If so something in your model is different.
2) Note, as an aside, the IDW does support the environment Mask setting which might eliminate the need to use ExtractByMask if you are only trying to clip all IDW outputs to the same mask area?