Matchmake servers aren't persistent. You have to pick matchmake servers which aren't persistent, or community servers which are persistent. Sorry. That's the deal.
BF3 and BF4 didn't have matchmake servers. If you want BF3 or BF4-like functionality, you need to use the server browser (just like BF3 or BF4) to join a persistent server. See the link I provided for a much more detailed discussion and why matchmake servers are not in a server browser and cannot be persistent without breaking their current functionality and reason they are used.
If you want to browse for servers, they need to be persistent. Like BF3 or BF4. If you want to matchmake, they aren't persistent. Like COD. The two are competing methods of handling servers. Both are in BF6. You need to make your choice.
Have cake or eat it.