Reproduction steps:
1) Open attached project "WebGL"
2) Build scene "Main" for WebGL
3) Enter play mode in the editor
4) Host a server by clicking "LAN Host(H)"
5) Run WebGL build
6) Connect to the host by pressing "LAN Client(C)"
7) Disconnect by pressing "Stop(X)"
8) Repeat steps 6 - 7 four times
--- After this point you will no longer be able to connect
--- In the editor you should see that the Connections list is full

Note:
--- Video of reproduction steps in user's original message.