Welcome to the forum. Thanks for your confidence in our services.
It's good to hear you have a level-headed perspective on this, but sorry to hear you're having trouble getting the answers you seek from your own physician(s). But there are no firm data on these questions, only clinical experience and judgment, so don't blame your gynecologist too much for not being able to give satisfactory replies. Mine also will be more vague than you might hope.
My first thought is that you make sure the recurrent lesions truly are warts, and not something else entirely; or perhaps increased perception of residual scars or hypertrophic (overgrown) skin that may periodically seem more prominent. Dermatology are the go-to specialty for genital warts, especially when atypical or if there is any uncertainty about diagnosis and management. If the current outbreak has not yet been treated (and maybe even if it has, if the warts have not completely gone), it would make sense to see a dermatologist.
My second thought is that you don't mention what treatment(s) have been used. You probably know there are several options, and any one of them is successful perhaps 60-70% of the time, and in general it is best to try other treatments after recurrence or in case of non-response. Also, combination treatment may be most effective, such as both cryotherapy (freezing) plus podofilox or imiquimod. I might have more to say on this if you'd like to tell me what treatments you have had and how each one went.
"We do use condoms" seems to imply you're monogamous in a committed relationship, yes? If so, then depending on its duration, your partner probably has been exposed repeatedly (despite consistent condom use) and perhaps infected. My general advice to committed monogamous couples is to not use condoms or otherwise go out of their way to prevent exposure and infection, but rather to be on the alert for symptoms (warts, regular paps in women) and seek treatment if anything shows up. Oral HPV isn't rare, but the large majority of oral infections don't cause overt warts. (On general aesthetic grounds, I can understand why you and/or your partner would prefer to avoid direct oral contact with warts, but if that's not an impediment, there is no reason cunnilingus should not be in your sexual repertoire. Of course oral sex by you isn't an issue.)
Unfortunately, the question about ongoing recurrences is the one on which we just have no good data. Clearly some people have recurrence patterns similar to yours, but there's no predicting who. There are no obvious differences in HPV type, other health issues, general immune system competence, etc. However, if you smoke, for sure you should stop. Of all the nutritional, immunity, and lifestyle conditions that might be imagined, only smoking is known to increase the rate of progression of pre-cancerous pap smear changes and clearance of HPV from the cervix. There are no data on warts, but I think it likely that smoking could be an issue some of the time. In any case, these recurrences probably will not continue indefinitely. Most STD experts, gynecologists, etc rarely if ever see patients who have continued with recurrences more than a few years. So assuming each outbreak is confirmed as warts, each episode should be treated aggressively until entirely clear and one day (maybe now) you'll stop having them.
Finally, to your closing comment: the appearance of a new wart does not mark the time when someone is likely to be infectious, e.g. for a previously unexposed partner. Active HPV probably is present and transmissible for weeks or months before visible warts appear. In other words, transmission often occurs in absence of visible warts. That's not necessarily good news, but it does mean you don't need to compulsively examine yourself every time a new sexual episode is on the horizon.
Excellent comprehensive information on HPV and genital warts is available from CDC (www.cdc.gov/std) and ASHA, the sponsor of this forum (www.ashasexualhealth.org). I hope these comments also have been helpful. Let me know if anything isn't clear, or if you'd like to fill in some of the details of your treatment to date and maybe clarification of your sexual relationship(s).