So I've found scattered information about progress missions (ayumilove doesn't say what is retroactive and various other sources I've found don't have parts 1-3 filled in much), but I was wondering whether any mission you've completed stays completed even if you don't claim it.  Specifically, on part 2, the second to last mission is to Reach Silver 2.  Now it definitely wasn't retroactive (since the last few days I've been bumped down to Silver 1 multiple times) but I got back to Silver 2 and I don't want to claim it yet.  If I wait until the next fusion to claim it, does the mission stay completed even if I've dropped out of Silver 2 again?

I mean, it seems like it should be a commonsense question but unfortunately most of the mission wording and structure is extremely counterintuitive so I don't want to shoot myself in the foot if the arena continues to get worse.  So if you are 100% positive on the answer, it would be really helpful.