There may be some transparent part of the UI overlaying the chat window, and depending where the links show up in the chat window that may prevent you clicking them since you are clicking the transparent UI window instead. That's about the only way the UI can interfere with links, once they are clicked it's up to the client to deal with them.
You can try to hit F10 to check if there are such invisible UI windows (only works if they have a background element, however), or wait until next time you cannot click a link, then either scroll it around in your chat window or move your chat window and see if it starts working.
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