If you spend a lot of time on Tumblr’s apps be sure you check your inbox every now and then. There are no push notifications to let you know you have a message.
Check your inbox/ask. Messages don’t always push to your smartphone.
I think for the new year Tumblr needs to revamp their messaging system. We need to have greater management of incoming and outgoing messages. I also think the follower/followed management systems need work too.
If you use Tumblr mobile don’t forget to check your inbox from time to time. I don’t think you get notifications about when new messages come in.