I have a honda with this engine, and no problems with it starting, maybe the choke isn't working properly. Mine has the choke lever on it, which is great because I know it is choking. If you don't have a choke lever on the handle then you have the autochoke, but I still haven't seen that problem with any of the ones that come into my shop. Have had ones with stopped up air filters that don't start up that easily or sound good.
One other thing I have seen on some of the hondas that come in for repair is that the carb insulator and/or gasket has been installed backwards and it will never run good like that.
When your mower does start, does the engine surge or anything or does it run smooth?