NCT TRACON Controller reported they vectored and turned an aircraft they temporarily lost radar contact with. The aircraft may have been below the Minimum Vectoring Altitude when flying the assigned heading.

Narrative

I was working the Toga Sector; had held SJC departures; and released a NUQ IFR departure; Aircraft X; on the only allowed heading of 345 degrees and 030. Aircraft X checked in climbing; and I observed the data tag momentarily at a good altitude to turn and the primary target. I advised them radar contact; turn right heading 120 to keep the flight inside of my higher MVA's 6-7 miles east. I lost the data tag almost immediately after this; and assumed because of the speed of the aircraft and fast turn I would re-acquire them in a moment. The tag did not acquire. After ensuring there was no conflicting traffic in the area I climbed Aircraft X to 050 to ensure terrain separation as I did not know where they actually were and advised them radar contact lost. I instructed them to reset their transponder and squawk altitude and still did not observe the aircraft beacon except intermittently or a primary target. I advised them I was unable to acquire or see the a/c and finally the equipment worked and the aircraft tagged up 5-6 miles east of SJC at 050. I am unsure of what Aircraft X actual position was until that point. I issued a vector that should have kept them clear of terrain and MVA's; but once I lost their tag my only option was to climb the aircraft to a safe altitude regardless of their position in the surrounding area.The departure procedure off of NUQ has been reported by myself and numerous co-workers multiple times. There are numerous issues with the procedure as the vector puts them in direct conflict with OAK arrivals worked by another area. The only acceptable option on departure is to turn them southbound once in contact with Toga; inside of the MVA's because Woodside owns 040 directly above us; and then climb to 050 when we are able. In this case; not knowing where the aircraft was due to an equipment failure after the initial vector required me to climb the aircraft to 050 to ensure terrain separation. I was able to do so because there were not other aircraft in the direct area where the aircraft was. In most other cases; there very well could have been an aircraft directly above the departure corridor preventing a climb because radar contact was lost. This situation is abnormal; but not impossible in the future. We have had multiple instances of losing communications with a/c departing NUQ as well. We need an acceptable RNAV procedure that turns a/c southeastbound on departure; ensuring immediate terrain separation and preventing conflicts with other sectors. Previous reports have identified these issues to the facility and the facility has decided not to act on them. Safety incidents will continue until this procedure is fixed.