It is not related to available space. It is a utilization issue. But like you, I do not know the details of how it is configured.
The idea is that there is a maximum number of "connections" that can be made to the database. On our site, those connections are made in these ways:
1. using the forum
2. viewing the site
3. users modifying their collection
4. using the mobile app
When that maximum number is reached, then you will get behaviour like this:
- too many connections error on the forum
- items not loading on the site (collection will have zero items, index won't show forum threads, etc)