I think if you’re gambling with a reputable company then you won’t have this problem. That’s what makes them a reputable company. If for some reason you do have issues, the first thing you need to do is make sure that you didn’t break any rules or do anything illegal. If everything on your end is good and your identity is on file with the casino, then I would first see if you can work the issues out with them. If not, then you can post exactly what happened here and see if the community can be of any help.
The problem is that there are gamblers who play on some mid tier casinos and obviously this is what they will get when they won big. There will be problems when they try to withdraw and will give every reason in the book not to processed or delay it. In your case if you really think that you didn't violate any ToS then you have every right to demand your winnings. As others have said, if they have a live support chat then talk to them and ask for the reasons why they are delaying your withdrawals. Just make sure to screenshot and capture every chat and logs and email.