Cessna Citation Latitude pilot reported both HF radios were inoperative during flight and indicated a suspected grounding issue was the cause.

Narrative

I was acting second in command (SIC) but flying left seat this day. On preflight I checked HF1 & 2 and both tested normal. Airborne; north of ZZZ; Center terminated radar coverage and told us to contact ZZZ1 ARINC. We tried to call ARINC on primary and secondary but both wouldn't work. We then called ZZZ Center back for different HF frequencies and told to try again. This went on 2-3 times back and forth before we completely lost contact with ZZZ Center. After lost communications we went to Jepp charts and found frequencies for ZZZ2 [Center] and contacted them. ZZZ2 Center specifically said who are you? Where are you going? I have no record of you in the system!". During this time I tried to press my opinion to turn around and re-enter radar controlled airspace since we had communication with ZZZ2. Then; we could fly on VHF in radar up the coast and divert to ZZZ1 to clear customs. My pilot in command (PIC) was indecisive and wouldn't make the call to divert. Eventually we lost communication with ZZZ2 on VHF and only had other aircraft to relay our calls back to ZZZ2 and eventually to ZZZ1 [Center]. We continued northbound towards ZZZ2; aircraft relaying our position reports. At one point the PIC then decided to divert straight west to ZZZ1 but I ran the time/distance/fuel/headwind numbers and it was more beneficial to head towards ZZZ2 and land there or even continue on to ZZZ3 since we had aircraft relaying our position. I sent an AFIS (Airborne Flight information System) message to the Dispatch in route explaining our lost coms on HF and the chief pilot responded with an acknowledgement. Once we reached the ZZZ1 radar coverage airspace of ZZZ2 the VHF radios worked as they should. ZZZ Center told us to contact ARINC and if it didn't work to come back. When we contacted Arinc on HF now the radios worked!!!! We then used HF radios until reaching ZZZ1 Center radar covered airspace. On landing in ZZZ3 my PIC called the chief pilot. The chief pilot told us that the Latitude is having an issue with HF radios. Apparently both HF radios have a common grounding point on the airframe that is subject to an intermittent grounding issue during turbulence; weather; changes in temps and that they know about it. If I remember correctly we then were told to write up both HF radios under the MEL and I believe we did so."