Post photos so we can help you. You can post them in the comments.

I've tried using tape but it's a temporary fix, not strong enough. I'd rather find a permanent solution

It sounds like a blockage in that vent line because that access door should not be popping out. There has to be some back pressure pushing out out.

Check the whole exhaust line including where it exits to the outside.

Oh interesting. I'm in a condo so not sure how to check the whole exhaust line. Once the blockage is cleared, what's the best way to seal the door?

There are two “male” clips on the panel, those should mate with the “female” clips in the opening.

Maybe the clips in the opening need to be “tighter”,

Does the door stay on when the dryer is off?

If so then the clips that secure the opening are fine.

I wouldn't permanently seal that access door. It's there so you can clean it out.

There are companies that can do that for you or if you're handy watch some Youtube videos and get an idea how it's done.

Yea I noticed the clips too but can't seem to latch them in. I'll try again. Thanks everyone!

Don't use the dryer again until you have unblocked the vent. Blocked dryer vents are the source of a lot a house fires.

I'm in a condo so not sure how to check the whole exhaust line.

If your vent is blocked, so may be other vents in the development. Is maintaining the vents the responsibility of individual owners? If not, then whoever is responsible is neglecting some important maintenance duty and needs to be addressed ASAP.