@tmtm4 I am a patient with dental implants, and yes, the success of dental implants depends on bone growth around the implant to hold it in place. Another thing they don't tell you is that they make the implant anchored teeth so there is no contact with the opposing tooth on the other arch. The reason for that is that the shock of bashing an implant with your other teeth causes problems like bone loss. Another problem is if food debris can be trapped up under the gums around the implant. These are things my oral surgeon said recently because I just went through oral surgery around one of my implants. I have good bone quality and a lot of bone in my jaw, and I got Zirconium implants because I have had reactions to metals in my body, and suspected that titanium implants could cause immune issues for me. That hunch turned out to be right, because when I broke my ankle and became the owner of titanium surgical plates, they did cause pain, and I had chronic hives for months and an escalation of my asthma symptoms.

We did everything right, after extraction, there was bone graft placed in the empty sockets and we waited 5 months for healing before the implants were placed. Then we waited extra time for my bone to fully integrate with the implants. I got my new bridge also made of Zirconium last summer, and a month ago, I developed a fistula that formed on my gum over the implant because of an infection there. My oral surgeon had to cut open the gums to figure out what was wrong, and it was just at the lower end where the teeth attach, I had bone loss and degradation. The rest of my bone is fully integrated and a lot of solid bone around the implants. He debrided away the dead bone, and replaced it with bone graft. I will see him next week to follow up from the surgery.

I see all these commercials on TV for implant supported dentures, and I have to think that those could be a recipe for disaster if they are taking all the pounding of chewing and are under the denture that can trap food debris. I was being careful with my oral care, and still got in trouble. In my case, it may be a defect in the abutment which is the go-between between the implant and the teeth on the bridge. There was a notch that showed on the X-ray, and perhaps that tiny defect was trapping food debris that caused an infection causing done loss. The oral surgeon should have something to say about this at the next appointment.

The other thing about implants is they are very expensive, and you don't want to spend money experimenting on something that may not be a good solution in your case with osteoporosis. There is a lot of money to be made doing them, so income for the dentist and surgeon may influence their decision to do them. It is a tough question to answer as to what is right for you. You definitely need an opinion that is honest and not biased by potential income to be made. I will try to remember to ask if osteoporosis is disqualifier for dental implants.
I did search for some research that wasn't an ad for a practice and found this:
https://meridian.allenpress.com/joi/article/41/5/550/6748/Low-Skeletal-Bone-Mineral-Density-Does-Not-Affect
Your rheumatologist makes a good point about your teeth falling out. One of the problems leading to this is receding gums because it is the blood supply in the gums that keeps the bone alive in the jaw holding onto the teeth. I have had a few gum graft procedures for just this purpose where they take a slice of gum from the roof of the mouth and insert it into the gums above the teeth on the outside of the arch. If this is a problem that you have, that will affect your bone quality in your jaw in addition to osteoporosis.

In my case, the oral surgeon is in a practice for just oral surgery and dental implants. He does not do the restorative work or make new teeth. That is done through my dentist and the dental lab. I think this gives a more objective opinion. It is not a "one stop shopping" practice to pull the teeth and replace them all at a great cost to you as outlined in a fancy brochure or commercial full of smiling people who are happy with their new smiles. You definitely need an unbiased opinion from a good oral surgeon and facial surgeon and perhaps that of a good periodontist about the health of the gums in relationship to the jaw bone.

Have you been evaluated by a periodontist about tooth loss?