There is no "too many iterations" in numeric optimization. "Too many" is what takes "too long", for a case-specific definition of "too long".
However, slow convergence (needing to increase the number of iterations from the default) is often an indication of potential problems. It could be that your data simply can't support the model and you need to simplify it. This is often the case if you have a complex random effects structure (as you do).
You should use the methods described in
help("convergence") to check that the warnings are not false positive and/or that you actually have achieved true convergence (arrived at a global maximum).
You should also carefully check the model output. Extremely small estimated variances (or strong correlations) of random effects are reason for concern (and often mean the parameter should be removed from the model).