Such a rule would disproportionally impact people who live in a different time zone than most other people on the site. (I know this post was first published on OB before threaded comments were implemented, but ISTR someone calling someone else out for making too many comments in a row as recently as 2012.)
A more reasonable rule could be “you shouldn't make more than n comments an hour” or similar.
There is no rule against commenting more than 3 times in a thread. Sorry if anyone has gotten this impression.
However, among the 10 "Recent Comments" visible in the sidebar at right, usually no more than 2, rarely 3, and never 4, should be yours. This is meant to ensure no one person dominates a thread; it gives others a chance to respond to others' responses. One-line comments that quickly correct an error may be common-sensically excepted from this rule.
You need not refrain from commenting, just wait a bit.