I use a Dot in my car and I've noticed that the boot-up time varies sometimes. But I think it has to do with my car's 4G LTE connection to the internet. It seems that the blue ring would continue much longer if the internet connection is not available immediately.
You did not mention if you also turn off your router and/or modem. I've had both DSL and cable internet before. Whenever the modem is powered off and powered on again, the time that it takes for it to get back online can range wildly between almost immediately to upwards of 10 minutes. If this describes your scenario, the Dot's blue ring will continue for as long as the internet is not available or until it gives up several minutes later.