OK, thanks for adding information. I guess there is no exchange of marked individuals between the cities, you are using a CJS model and you are interested in comparing the apparent survival in the two cities. A situation like yours occurs very often in Ecology - the homeland of the unbalanced designs - and not just in capture-recapture analyses. I don't think there is any way to solve it, neither in MARK nor in any other environment. The sample size (see
here to get an idea of what it is in capture-recapture) affects the precision of your estimates and, therefore, your ability to find "effects".
In general, I do not see why the difference you have found should be a statistical artefact. The way the unbalanced design affects your testing hypothesis is by influencing your power to detect a difference between the apparent survival in the two populations (if in one city your sample size is not enough, to put it in some way). Otherwise, the unbalanced design should not create a spurious result unless there are particular problems on other sides, such as a very low recapture probability (<10-15%) in one of the two cities which may bias the apparent survival estimate. If you did not find a difference between the apparent survival of the two cities and you suspected it was not so, you could have done a power analysis to see what effect size (what difference in apparent survival) the model would have been able to detect with (the distribution of) the given sample size. For this purpose, you would have needed to repeatedly simulate and analyze data from your model estimates to see how many times you find a biologically relevant effect (contrasting, by AIC or whatever else, the model with and without the city effect). I see many caveats to this procedure, one of them being the fact that you never know how well your data (and therefore the parameters' estimates) represent the ecological process (of which they are just one specific outcome), but this goes beyond the scope of your question…