This seems more of a general database question than one specific to SQL Developer. The reconnect capability in SQL Developer (whether triggered automatically or explicitly requested) refers to a database connection (possible a shared connection), not the number of open database links.
You did not give the actual Oracle error message number, but it seems the reference is to the static database initialization parameter OPEN_LINKS. This defaults to 4, has a max value of 255, but cannot be altered without also restarting the database.
Probably what you want to do is described in the following Ask Tom discussion: Ask Tom &quot;open_links parameter&quot;
Note his comment about using dynamic references, not static references, to SQL statements containing DBLinks.
SQL Developer Team