A very devout Catholic that is knowledgeable in Catholic teachings told me that the annulment tribunals would normally allow a person two mistakes; two annulments. Generally he said a third annulment would be refused. This doesn’t make sense to me. If someone is married three times and each marriage ends in divorce, doesn’t this pattern make it look like this person had no intention of honoring his or her vows. If a person has no intention of honoring his or her vows before the marriage has taken place wouldn’t this be grounds for annulment. Therefore the person that is asking the annulment tribunal for a third annulment I would think he or she would have grounds for a third annulment because they never intended to honor their vows.
I would ask that very devout Catholic to show you some evidence, namely from Canon Law, that this is the case. Annulments are not exactly a cut and dry thing–if there were grounds for annulment in three cases, then there would be three annulments granted. If there were not grounds, there wouldn’t be. Ask your friend to show you some evidence of this, or to clarify if perhaps he meant something about general practice or general thinking on the part of tribunals. If the latter is the case, then ask your friend where they get their information about how tribunals think.
-ACEGC
I think what you’re saying is that this person proves that he (or she) haven’t taken wedding vows seriously in the past, so why believe that they would do so in the future? If I had met someone who had two annulments, I’d head the other direction. I’ve been through one, and don’t want to repeat the process. In fact, after two annulmens, I think that a priest would have doubts about doing the ceremony.
This was my thought too.
As to the matter in the OP…and in deference to the OP sating the person is knowledgeable…I would say that IF (a very big if) such a thing exists, it is more a matter of custom contained within a given tribunal. Not something that is written out.
Each annulment request is unique and must stand or fall on it’s own merits.
Peace
James
I may be wrong, but I thought I heard that a declaration of nullity can be made in such a manner that one or both are NOT automatically eligible to marry again.
Via the keys of the Kingdom, the church holds the power to bind and loose. It doesn’t seem unreasonable to me that a Tribunal could require an extraordinary level of marriage preparation and the concurrence of a competent authority before releasing a person or persons to attempt marriage again. After all, if someone proves over and over again that they lack the capacity to consent (for example), then doesn’t the church owe it to the next potential spouse/victim to ensure that this person has overcome his/her impediment?
Or I may have imagined the whole thing! It’s hard to tell some days… 
You are correct.
The tribunal had put a prohibition on my reciept of the sacrament of matrimony pending counseling by the pastor of my parish as part of the decree. The tribunal can order additional classes and other preparation if it so desires.
You are not imagining anything.
-Tim-
This is a question for either moral theology forum or sacraments forum.