You only pay that fee once to open the channel to the LSP and then can use the channel until it is closed. I have been using Alby Hub for a few months and not had any channels closed on me.
There are a variety of reasons a channel could be closed and you can get some info here:
https://guides.getalby.com/user-guide/alby-account-and-browser-extension/alby-hub/faq-alby-hub/why-was-my-lightning-channel-closed-and-what-to-do-next 

 Which LSP you're using?  

 I have a channel with Megalith and LNServer.