Your symptom is non-specific, and could theoretically reflect a variety of different issues. One question that would be helpful to answer is whether the pain that you're currently experiencing is due to the same underlying cause as the pain you experienced with your previous crown, because the second crown eliminated the presumptive cause of the initial symptom (i.e., the food impaction). Although the food impaction is undoubtedly a potential etiology in dental
pain, it does not logically follow that just because there is food impaction that it is the cause, or the sole cause, of the pain. This leaves open the possibility that there is an ongoing issue that has yet to be identified or managed.
It is tempting to suspect some deficiency in the new crown, especially considering the repeated loosening-- a crown that falls off just two days after being cemented would seem to have an insufficient amount of the quality we dentists call "retention"-- the ability to reliably stay attached to a tooth. A crown with poor retention can break free of and move on the tooth in response to chewing force, and this movement can irritate the gum tissue and the surface of the tooth. Therefore, the crown itself is certainly not above suspicion, and needs to be evaluated. It is also evident that your dentist has already done enough "adjusting" of the crown to have determined whether that strategy is beneficial, and it is time to move on to additional diagnostic inquiry.
So, what needs to be done is to re-assess the condition and quality of the crown, and the pulpal, periodontal, and structural condition of the tooth, because all these parameters have the potential for eliciting the symptom you describe. If your dentist is either incapable or unwilling to re-assess the fruits of his labor, you will have no choice but to continue the diagnostic inquiry elsewhere. As for your perception of the insurance "frequency limitation"-- you should know that it does not pertain to a particular tooth per se, but to a particular service on a particular tooth. In other words, although your insurance benefit for another crown on that tooth will have been exhausted (typically, for a period of 5 years), you would still have reserved benefits for other services that are different (e.g., periodontal, endodontic). And at the very least, you will want to move forward with diagnostic service so a clearer picture of the problem emerges.
Therefore, and based on a general truism that a considerable majority of complaints like yours are caused by pulp
inflammation (a feasible assumption, given the potential for pulp injury following two consecutive crown preparations), your best first strategy would be to consult with an endodontist (root canal specialist). This type of clinician is particularly attuned to these types of symptoms, and with his training, experience, and intuition (not to mention his lack of personal culpability in your current situation), would be best able to provide an informed and candid diagnostic assessment. You can find contact information for an endodontist near you by consulting the online directory of the American Association of Endodontists
Hope this helps...