The debate for each amendment is timed. However, there is no limit to the number of ‘relevent’ amendments that can be introduced.
I agree that there isn't a numerical limit, but the total time for debate (regardless of how many amendments come into view) is 20 hours, maybe a few more to account for the time of day or last minute bitchin'.
So, there is a practical limit, and that limit exists two ways. First, by the total time allotted to consider reconciliation; and second, by the limited power of any given Senator to call amendments up for debate under Senate rules.
When this "number of amendments is unlimited" meme surfaced, I looked at the rules cited for the proposition, and they are no different than Rule XXII which provides for 30 hours of post-cloture debate, or any number of other statutory time limits for considering certain types of legislation.
Heck, under normal rules, any single amendment is entitled to unlimited debate - which as a practical matter triggers the use of cloture to get over objection - so a string of new amendments spaced about 4 days apart would have the effect of blocking action, even if 60+ Senators object to the blocking. The way this "normal rule" is suspended is to say "20 hours of debate, total, do whatever you want with your 20 hours." Otherwise the 20 hour time limit would be without effect.