It would clearly help if you stated what software you are using. I woud put that in the title. I think you are speaking of HFSS, in which case someone with knowledge is more likely to look at the post if you put "HFSS" in the title.
Have you actually made all 6 faces a radiation boundary? If one is left PEC, you will get problems. Does the delta S plot seem to be converging nicely. You might want to increase the number of iterations above the default value of 6 and make sure it stays converging. If it starts to diverge, that would indicate a problem.
You should try limiting the size of the tetrahedrals to be be no more than lambda/6 on the boundary.
Remeber if you solve at 600 MHz, but sweep from 300 MHz to 1.2 GHz, the airbox needs to be 250 mm away from the antenna since the longest wavelength used is 1 m @ 300 MHz.
The size of the airbox is more critical for measuring the radiation pattern that it is for measurement of return loss.
If you post your model, someone with access to HFSS might be able to help you.
Dave