I easily spent 200+ hours in the shop during build when I was a student; I'd have to see if any of my time logs are still around my house for an exactish number. Others spent more time.
Now, where the administration is coming from: They have a policy that limits time on extracurriculars. You guys are exceptions for now. Policies don't like exceptions as a general rule. So, they're working on limiting the exception. They're probably also a little concerned about health, grades, etc.
There is also a valid reason to limit time in the shop: You need time for family, homework, sleep, etc., regardless of whether you think you do or not. My college recently implemented a policy on their engineering teams: Nobody in the lab between 2AM and 7:30AM, or something like that. This was to keep us all sane. Could it be bent? Yes, near competition. But only if you were doing well in school, health, etc., and weren't doing it regularly. Teams are actually more relaxed now, and doing better work.
What I would suggest is offer a counter-proposal: Lab open 3-7 on school nights (6:30 is good, but see if you can get an extra half-hour to clean up), open to 10 on weekends, don't restrict student time
yet (emphasis on yet, because we'd like to get a fairer estimate of time). Track every student's time in the lab for this year. Time off-site designing and programming and such like doesn't count, but it would be a good idea to monitor that also. At the end of the next build cycle, total up the hours and come up with an average and a grand total. Round up to the nearest 25 for ease of tracking, and set that as the base limit. Do not count time working on homework in the lab--homework is important and not robotics stuff. (And if a student is being unproductive, i.e. messing around, count that time not at all.)
Request variances at the start of the school year based on how many students are reported on the team; that is, we know it takes about this many man-hours to complete a robot, we have this many students available, therefore, this is how many hours a given student can be expected to put in. Repeat the time-gathering every year to get better data; for example, a one year you might build a kitbot and the next year you might build unobtainabot that takes 10x as many hours to build, and a straight time-log won't show that.
Also, propose exceptions/extensions that can be applied for: if a lot of help is needed to finish on time, the team should be able to request extra open time, not to go beyond midnight on any given night, for up to two weeks in February. Students should be able to request up to two individual 50-hour extensions towards any time limit provided that they are in good standing. This is to help the robot do well at competition, and thereby show the school favorably.

(Robot not do so well at competition, school/sponsors might not look quite so great.)