Technically no. But you'll find you start running into page rendering issues if you have too many comments on an issue.
In the last place I ran into issues with comment numbers, a rogue script had commented around 3,000 times on the issue. The issue never finished rendering. That system started to get slow at around 300 comments, but to establish an acceptable limit for your system, you'd need to test it on your hardware and network (That was JIRA 4.2 with 18,000 user accounts and half a million issues, running on some decent hardware at the time, but it was 3 years ago)
I can back up on what Nic said, there is no limit. We are using the ORASI Plugin and it had a bug that commented 14,000 times on several tickets.
The ticket rendered very slow, we have a very large JIRA instance too. You can create a ticket against Atlassian to have this configuration, seems reasonable for me.
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