Don’t take it personally
You may find out about the loss of a client via a number of routes; the client may tell you, they may just stop paying you or they may just cease replying to your correspondence.
Whichever way you hear about the loss, don’t take it personally. Part of the life of being a business owner is to take the rough with the smooth and losing clients, sadly, is just part of that rough. Put on a brave face and deal with the loss; there will be time to reflect later.
When you find out that a client is moving on, the best approach is to act professionally. Avoid getting into a heated debate with the client about their decision and whatever you do, do not tell them they are wrong even if you think this is the case.