This may happen due to following reasons:
1) You have a high resonant structure at your meshing frequency (try to mesh at slightly higher frequency and run discrete frequency sweep).
2) You S-Parameter (or delta energy in some cases) convergence criteria is very low. Default is 0.02. I sometimes go for 0.01 when I really want to push the mesh.
3) Try mixed order basis function instead of first order.
Also, what is your definition of "too many passes". I usually set my default max to 20. (Sometime 40 based on complexity of model).
How much RAM do you have? Sometimes the computer in not powerful enough (in terms of RAM) to solve the level of complexity of the problem. So you might have to try this on a bigger machine (more RAM).
Hope this helps.
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