It is so frustrating, I know. I have not heard of an instance where failure to enroll during enrollment was waived due to the fact that coverage was needed for a medical condition in the Medicare Scenario. I suspect that is because nearly everyone has a medical condition for which they need the coverage. That said, bugging them costs you nothing, so while you research a suitable policy you can handle stil. 7/2016, I'd go at that angle as well. Flukes happen. And, ObamaCare open enrollment may be starting Nov. 15 (not my specialty, but just happened to hear of it). Since you NEED to have coverage, I think you really need to consider looking at these other options. When we ourselves decided to look to change insurance, by looking into the "marketplace"/exchange, we did so by meeting with an insurance agent (in our case, it was BCBS) and he actually showed us policies from many companies, explained the bronze, silver, etc. plans and did not himself sell us anything. We signed up ONLINE, and that is what he sought to explain.
Now, that said (that I think you should utilize all avenues), going back to the issue of reinstatement, look at this:
Scroll down to 408.100 etc.
Review your dates and see if you can appeal and get reinstated based on this section.