I'm not going to take sides on 'what language to learn next.' You've not given us enough information on your codebase, the size and nature of your company, etc. I would say a rewrite is as likely to put you out of business than not, but that's ultimately your choice and unless I know all the factors I can't tell you if its a risk worth doing.
Regarding the link you gave on Perl 'ossifying', there was actually a signification discussion on the Perl Reddit about that article which I want to point out:
I would say the website that generated that article seems to be some sort of SEO play (they just have a bunch of articles on stuff that has some interest and controversy) and they stick ads on it. There's nothing mentioned in it that hasn't been mentioned 100K elsewhere (including here on Slashdot).