Cessna 210 pilot reported a gear up landing due to being distracted with radio communication issues.

Narrative

I departed ZZZ1 enroute to ZZZ in Cessna Centurion T210 IFR with no passengers. On arrival I requested radar vectors to the RNAV (GPS) Runway XX approach. While I was being vectored; I noted a complete loss of radio communication with Approach Control. I did not hear a vector to the final approach course and no clearance for the approach. The failure was intermittent and I could hear a word or two intermittently. Multiple attempts at restoring communication were not successful. I re-positioned the aircraft back towards the airport and managed to establish some communication with a Controller intermittently. He vectored me around some traffic and then cleared me for a visual approach to Runway XX. Unfortunately; the communication difficulties distracted me and I failed to lower the landing gear. No gear warning horn sounded. I had the gear warning horn worked on about ten days prior to this flight. A gear up landing was made with no injuries.Partial radio failure intermittent [was] due to poor connection of headset. No FARs violated. Distraction and failure of gear warning horn resulted in gear up landing.