I'm in a completely different part of the world (North-Western Europe, USDA hardiness zone 8), so take my advice with a grain of salt. That said, I'd leave the plastic in place over summer. You say it is a somewhat colder place with swings in temperature. A hoophouse buffers nighttime temperatures somewhat and helps it raise over day. It is a good to adjust ventillation in hotter periods, so you don't overheat the veggies.
Is it possible for you at all to differentiate between crops? You say you have a mix growing in there, but it might help if you plant heatlovers (tomatoes, cukes, peppers, melons etc.) together under the hoop, because the cabbages and onions etc. can fend for themselves just fine without the plastic and might be harmed by prolonged heat.