Take a look at the runtime settings for you app. This error generally means that you currently have enough active users to surpass the (number of maximum processes x number of connections per process).
The fact that you get it on refresh is just a nuance of the fact that web browsers don't guarantee the ordering of open/close events, so RSC sometimes sees new connections arrive before it's seen your old connection close. In those cases it can be off-by-one for a narrow window as your page loads, in which case you might hit this error every-other refresh.
But the heart of the problem is just that you need to increase the number of processes for this app, increase the maximum number of users per process, or add another RSC server and load balance across them.