A TRACON Controller reported they left an aircraft on a delay heading too long and it flew below the Minimum Vectoring Altitude.

Narrative

I was vectoring Aircraft X in for an ILS to Runway XX at ZZZ. The Tower called and advised of a wind shift and a need to utilize Runway XY. I advised Aircraft X of the issue and then vectored the aircraft to the East to set up for the RNAV-A approach. The aircraft ended up going around and coming back to me. I put the aircraft on a vector of 280 and told the pilot to maintain 8000 ft. The Pilot told me they wanted to try the ILS to Runway XX and circle the Runway XY. ZZZ Tower told me that they had 2 aircraft ready to go and then I could bring Aircraft X in opposite direction. I told the pilot of Aircraft X this; so he would know the plan. Initially I had only planned on ZZZ Tower getting one of the aircraft out; before I brought Aircraft X in; but the said they needed to get the other aircraft out as well. I completely forgot that I had out Aircraft X at 8000 ft. Because of the fact that I released both aircraft off of ZZZ; I had to keep Aircraft X outbound on a vector. I realized that the aircraft had entered a 9000 ft. MVA at 8000ft and had been in the MVA for approximately 7 miles. I told the pilot to turn east and climb to 9000 ft. I understand that it was my own expectation bias and then failure to change my plan that caused the issue. Aircraft X landed without incident.This was completely on me. In hindsight; if I had kept the aircraft level at 9000 ft. or even allowed them to climb higher; this would not have occurred. Also; after the pilot advised that they wanted the ILS I could have easily held them at ZZZZ which I have done in the past. I was too slow in realizing the error in my decision to have the pilot level off at 8000 ft.