I know the short answer is "whenever". So does this mean if someone paid cover to get in somewhere it would be legal for them to be kicked out the minute they step inside (and didn't do anything)?
I noticed a sign at McDonald's saying people are only allowed to stay inside for 30 minutes and can be removed at managers decision. So if someone bought $100 from a fast food restaurant and sat down to eat it, they can still be told to leave? Is this actually within policy of McDonald's?
When you give the owner of the establishment your money, you are executing some of your obligations pursuant to a contract you are creating that binds you and the business owner to certain terms - whether you are paying cover to get into a club, or paying for 100 cheeseburgers at McDonald's.
Typically, you aren't going to get a written contract up-front with all of the terms and conditions that both sides are agreeing to. Contracts require a meeting of the minds to occur and, when terms of the contract are unclear, they are either held against the drafter of the contract (if one party did most of the writing of the contract) or judged based on concepts of equity, fairness, and what a reasonable person entering into such an agreement would expect.
So - what of your examples?
If you pay cover and get into a club, and "didn't do anything", presumably you would not have violated the terms of the contract that was created when you exchanged your money for access to the facilities. Their throwing you out regardless would constitute a breach and entitle you to be made whole (e.g., a refund). If they were found to act in bad faith they might even be guilty of more - either owing more to you, or fines to the government, or maybe even getting criminal charges pressed (e.g., fraud).
If you bought $100 worth of burgers at McDonald's, the situation is similar but perhaps less clearly tilted in your favor. When ordering, did you order at the counter or at a pickup window? Did you order for "here" or "to-go" when the order was placed? A judge may side with McDonald's since it may not be reasonable to eat $100 worth of food at McDonald's in a single sitting. Of course, if you can show that you made it clear you intended to stay before you exchanged money for product and that this was a part of the agreement, that might be enough to get the matter settled as a matter of contract.
When in doubt, ask yourself whether you are acting reasonably and in good faith, and if the other party is acting unreasonably or in bad faith. If both are true, you are probably entitled to be made whole - in the sense that you will be restored, at the other party's expense - either to a state prior to the agreement, or to the state you would have been in had the other party upheld its obligations.
In any case - the owners of private property can always legally require that you leave the property. What's at issue is whether they are also entitled to benefit from your having honored some of the terms (payment) of an agreement that they later chose to terminate (without just cause). You might be entitled to a refund, but you won't ever be entitled to stay against the wishes of the owner.
If you paid to enter, you have entered a contract, and I doubt that you can be thrown out without a good reason, and without a refund. It's quite possible that it is legal to throw you out without any good reason, while giving you a refund.
It rarely happens because the business loses money that way, and the person removing you, unless they are the business owner, might lose their job over it. If your ex boy/girlfriend is the manager of the local McDonald's, it's probably legal if he or she doesn't let you enter, but if you complained to Ronald McDonald they might lose their job.
