Save IDs are stored on the server as unsigned integers, so the server can store up to 2³²-1 saves, or 4,294,967,295 saves. There are currently almost 700,000 saves, that puts it at about 0.016%, we can carry on for some time.

And, as jacksonmj mentioned, we have had some issues in that past where we reached the maximum number of files due to limitations in the file system that I have since moved away from.

The only potential problem for the future may be file storage and bandwidth costs. I have recently brought in a new server to take load of the other by caching static content.