Amelia,
I do agree with you, you should not increase the convergence criterion. Actually it seems allready a little bit to rough for your model.
What about the problem class you use? Is it a confined or unconfined model? Allthough most models are unconfined in nature, it maybe helpful first to calculate a confined model. Maybe the difference could be neclectable for a regional scale.
The solving of the problem should be more easy in a confined model. So you could try first to solve it for the confined case. Analysing that solution you maybe detect some problems in your model (e.g. some inconsistend BCs ...). Also this could give you better starting heads for the unconfined model.
In using an unconfined approach, I made some good experiences with the "phreatic" option. Here you can force more stability in the solution by increasing the parameter for the "residual water depth" in the "specific options" settings. This water depth should be somehow related to your vertical discretization.
Unfortunately FEFLOW gives no control over spatial distribution of occuring errors an convergance problems. But if you check your results carefully you will find places with strange hydraulics which indicates normally also numerical problems.
The most frequent error source in models as yours are the boundary conditions. You could try to eliminate them step by step and run the model to find out which one makes the most problems.
Zebra