Do aws free-tier t3.micro servers have a max?

According to the free tier documentation [1] you get 750 hours per month for free for the first 12 months of your account. 750 hours per month generally equals a full month of usage. Therefore according your description, if you plan to run your instances 24x7, then you would get 1 instance for free and the other you would pay for.

[1] https://aws.amazon.com/free/?all-free-tier.sort-by=item.additionalFields.SortRank&all-free-tier.sort-order=asc&awsf.Free%20Tier%20Types=*all&awsf.Free%20Tier%20Categories=categories%23compute&all-free-tier.q=ec2&all-free-tier.q_operator=AND