There have been many reports in various i3 forums, groups, etc., about what seems to be a higher rate of flat tires than normal. The 20" summer tires may be somewhat more flat-prone than the 19" all-season tires. Some who have had several flats have purchased tire warranties from tire dealers that sell the i3's Bridgestone tires, not from BMW dealers who want to sell expensive insurance that covers tires and wheels.
Using the included tire repair goop doesn't always work, is expensive to replace, and can cause problems with the tire inflation pressure sensors and even the tire itself, which can result in the tire being replaced rather than repaired. Calling BMW Assist usually results in one's i3 being towed to a BMW dealer even if the dealer is closed. Many BMW dealers will only replace, not repair a repairable tire, so the cost of dealing with a flat can be more expensive and time-consuming than necessary, especially because replacement tires aren't always available immediately.
I will be buying an inexpensive tire repair kit when I return to where my i3 is in storage. Many have had success sealing a tire on the roadside with one of these kits so that their i3's could be driven home or to a tire dealer instead of being towed to a BMW dealer. This could greatly increase the odds of having the flat repaired quickly and inexpensively rather than waiting for an expensive new tire to arrive.
Unfortunately, I think the problem is real and that you aren't just having bad luck. I have had low rolling resistance Bridgestone tires on our Honda Insight hybrid for 13 years and over 50,000 miles without a single flat, so I know that Bridgestone knows how to build low rolling resistance tires that don't puncture easily. It's difficult to come up with any explanation other than the i3's tires are to blame.