@Kyle448I'd say in and of itself, it's not a danger sign. I've stayed with hosts who send thanks for booking messages and those who don't, and I've never had a bad experience. That being said, I do send them myself, because I think it's just common courtesy.
I would look more at the host's overall track record. Do they have good reviews? Do they have many reviews? If the answer is yes, I would worry less. If this is a newer host, I might be getting concerned.
If you've asked specific questions and they're still not getting back to you, I would see that as more of a red flag also, but not everyone hosts all the time or always has access to the internet. Maybe they're travelling. I was on vacation a few weeks ago, and due to some personal stuff that happened, I wasn't as responsive as usual. Also, if your reservation isn't imminent, the host may not see your question as being pressing or in need of an immediate response.
If they seem to be good hosts and they're not responding and you need a response, I would consider reaching out for help from Airbnb before cancelling. Cancelling costs you money and you may be missing out on staying somewhere great.