I would add, that you could try to gently pull that plate and see if it goes up (just gentle pull without trying to then push all the way up). It's possible that some debris is lodged in and keeps it from moving up. I don't know if this plate has electronically controlled time delay or there is just a mechanical escapement. This is first time I'm reading about such a problem, so it can't be common.
So, to repeat, a gentle pull (with finger) towards you will not hurt anything, so long as you do not force it, just slight nudge and see what happens. If it does pop up, then try releasing shutter seeral times to see if it hangs again or not. It does not cost anything, so worth a try.