Yes, it happens. Especially for a business with an ongoing relationship with visiting customers, on a continuous service or a frequent service basis. Such as a program of monthly activities, or ongoing visits from the same frequent customers, even bars, restaurants, and retail stores, not tolerating bad behavior or payment problems from repeat customers. It’s good if you’ve never heard of it, as it indicates that you’ve never needed to. 
A suspension is not the first step (in a well run business). It’s the next to last step before cutting ties altogether, if things don’t change. There have been prior communications about the issue that haven’t been fully successful in encouraging the customer to change (if done properly, no idea about the thread-subject situation).
A suspension can be a shock warning that the situation won’t be tolerated further, without bouncing the customer outright. It becomes the customer’s decision to comply, or not.
This may not have anything to do with the FB kerfuffle, don’t know – Sometimes a continuing customer is a bit gaslight-y when asked to make an important change to fully adhere to policy (whatever it is). They partially change, or they make the change some of the time, but basically they maneuver to continue whatever irregularity they were doing as much as possible.
The business becomes increasingly exasperated by constantly having to follow up corrective action, or lose the policy line they are trying to hold. The irregular customer can affect other frequent customers as well, as the others become aware of it (they will). The longer the irregular situation continues, the longer this customer starts to stand out to the business as an outlier. Because of the constant need to follow-up when the other customers are following the policy.
I know of a monthly activities business who gave this same warning to a two customers just a few weeks ago. Turned them away from an activity until a long-standing irregular situation was fully corrected. The customers did correct, now everyone is behaving well toward each other as if it never happened, and no problems since.
Obviously a suspension isn’t done lightly. It’s for businesses who have decided they do not want customers who aren’t in line with whatever policies the business holds most firm.