The way that Linux handles system resource consumption is that on a per user basis it tracks how many threads are open to prevent abuse by any single user. This allows the system to operate effectively when there are many processes running especially by multiple users.

However in this case you want to increase that limit and that can be easily done by the following command:

ulimit -n 8192

If you encounter that error again you can upgrade it further as long as there isn't any contention on your system. Otherwise you may have to increase it further and also at some point resize to a larger Droplet.