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Well, that sounds something like Robot Jox, but it's complicated because the whole "recover lost mech" plot sounds like the plot of Robot Wars, a different movie though billed as a Robot Jox sequel. I doubt it's what you're looking for because the training stuff takes place in Jox and the apocalyptic wasteland takes place in Wars... I'd say you conflated the two films, perhaps watching them back-to-back, but the climax in Wars is nothing like what you described, and takes place with an entirely different cast of characters anyway...???
Does anybody remember the name of this film? It starts out, (obviously) in the future (although, the film itself looks like it was made in the 70's). There's spacesuit looking clothes, mechs are the main choice of vehicles, etc. The main characters are running an obstacle course as part of they're military-mech training, (that looks strikingly like the metal geometric half sphere, made from smaller triangles they had at recess when i was a kid), but room by room going down. Designed to help them get into there mechs as quicky as possible. The next day, the main characters (a male and a female) are running late for training, because they making-out! Meanwhile they're base get's hit and they get separated from the rest of they're team. The Big-Bad destroy's that base and every other base and the result is: post-apocalyptic world. Fast-Foreward, the main characters are still together, but struggling to survive. The guy remembers where a mech is (from before the apocalypse), that fell into a sinkhole and convinces her to go with him. They pack-up splunking gear and the equivalent of a mechanic's tools, but for mech's and head-out. They finally get there and spulunk into the sinkhole, but they have to leave some of the tools up-top, because they can't fit. They reach the mech and nearly fix-it-up, she splunks up to the surface to get something they need to finish fixing the mech just as the same Big-Bad (in his mech) is walking by. The Big-Bad see's her and tries to step on her. She does everything she can to dodge him from stepping on her, while staying beneath his mech to prevent him from shooting her. She manages to get the tool needed to fix they're mech and splunks back down, landing on top of they're mech and finishes fixing they're mech. He starts it up and I forget how he gets it out from the sinkhole to the surface of the desert, but he does and the old mech beats the new mech. The End. Anyway's, I can't remember the name of this film and hoped someone else does. Thanks!