Hi benjie, welcome to the forum.
You can pop over to Rhodes to renew your visa, however, when the hydrafoil is not running from Fethiye you have to go from Marmaris, which is about a 4hr drive. Last year the price was between £35/40 each so soon adds up. You can apply for a residency Visa up until the last day of your 3 month entry visa and would suggest, in the long term that this would be more economical than the continual trip to Rhodes.