A C182 IFR TO MAF FROM SAF THINKS THAT THE ARTCC RADAR CTLR FORGOT TO HDOF HIS ACFT TO THE NEXT ARTCC. RADIO CONTACT WAS WEAK AND THE CTLR QUESTIONED THE ACFT CLRNC. RPTR THINKS CTLR DID NOT REALIZE HE WAS IFR. HDOF WAS MADE TO ZFW AND REST OF THE FLT WAS NORMAL.

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MISSION WAS FILED IFR SAF TO MAF. CLRNC RECEIVED FROM SAF TWR WAS SAF V83 CNX V68 ANEEL DIRECT GOMIT MAF. ZAB ACKNOWLEDGED US AFTER TKOF FROM SANTA FE. WE PASSED THROUGH ANOTHER CTR SECTOR AND ROSWELL APCH; BOTH OF WHICH USUALLY RESULT IN A HDOF WITHOUT RADIO CONTACT FROM CTR. WE WERE SQUAWKING AN IFR CODE OF XXXX AND THE XPONDER SHOWED FREQUENT INTERROGATION AT A RATE NORMAL FOR THIS RTE. AT XA00 HRS I ASKED ZAB FOR A RADIO CHK AND WAS TOLD 'LOUD AND CLR.' AT XA10 I ASKED IF THE HDOF TO ZFW WAS PLANNED SINCE ZAB WAS BECOMING WEAK ON THE ASSIGNED FREQ. THE CTLR WAS OBVIOUSLY CONFUSED AND WAS NOT TRACKING ME AS IFR TFC. HE ASKED FOR READBACK OF MY CLRNC AND THEN HANDED ME OFF TO FTW. FTW ASSIGNED A NEW IFR SQUAWK AND A NEW CLRNC. FLT COMPLETED WITHOUT FURTHER INCIDENT. AT NO TIME WERE WE BELOW ABQ RADAR COVERAGE AND WE COULD HEAR CTR RADIO TFC WITH OTHER ACFT AT ALL TIMES SO I DON'T UNDERSTAND HOW CTR COULD LOSE US. HAD THIS BEEN IMC RATHER THAN TRAINING IN VFR FLT CONDITIONS; THE CONSEQUENCES COULD HAVE BEEN SERIOUS.