How many transfers?

Is there a maximum number of times a player can transfer on one hand?  My partner and I earned an unexpectedly good score on a board from last week's STAC games where I assumed that the number of transfers was limited. I quite arbitrarily applied a three strikes rule.

I picked up the following, at unfavorable vulnerability and second seat: ♠J4 ♥AKT63 ♦A92 ♣765.  Dealer passed.  We play a 12-14 notrump and, although we don't typically open 1NT with a five card major, for some reason I did this time.  LHO bid 2♣ and partner bid 2♥, a transfer.  RHO now doubled and I passed.  Lefty passed and partner redoubled.  I did recognize this as a re-transfer, although I was probably going to pass it if it came to it.

Incidentally, I discovered long ago, that it doesn't pay to re-transfer with a redouble unless you have at least invitational strength - just in case partner decides to pass the redouble out.  Better to just bid your suit with a weak hand.

In any event, RHO bid 3♣ and I passed again.  Now, partner bid 3♥.  Should I have known this was another transfer?  Perhaps.  I thought partner had finally decided to support my hearts and this was to play.  Partner's "thank you, partner" had just a smidgeon of an edge to it, I thought.  The defense was not optimal and my partner's declarer play was brilliant so he brought home this unlikely contract.  His hand, by the way, was ♠AKT763 ♥52 ♦T753 ♣4.  One pair did beat us by taking ten tricks in a spade partial, but our result was an excellent 10 out of 11.