Instance stuck on blue login screen

Can you check the system log of the EC2. Go to EC2 console > select EC2 > Actions > Monitor and Troubleshoot > Get system log. This log will tell you if the EC2 is ok or not. Also, if you have enabled SSM, see if you can login to the EC2 using SSM or Fleet Manager.

The issue you're experiencing with your EC2 instance getting stuck on the blue login screen is a known problem that can occur for various reasons. Here are some potential causes and solutions:

1. Resource constraints: Even though you're using a t3.large instance, which has more resources than smaller instance types, it's possible that the instance is running low on memory or CPU, especially if you have resource-intensive applications running.

2. RDP service issues: The Remote Desktop service on the Windows instance may be encountering problems between sessions.

3. Windows updates or background processes: Sometimes, Windows updates or other background processes can cause the login screen to hang.

To resolve this issue, try the following steps:

1. Check the instance's system logs and RDP error logs for any specific errors that occur during connection attempts. You can access these through the EC2 console by selecting the instance and choosing "Actions" > "Monitor and troubleshoot" > "Get system log".

2. Ensure that the RDP service is set to start automatically. You can do this through the EC2 instance's settings or by using AWS Systems Manager.

3. Verify that your security group allows inbound traffic on port 3389 (RDP) and that your Network ACLs are not blocking the connection.

4. Try connecting using the latest version of the RDP client, as older versions can sometimes cause issues.

5. Attempt to connect using the "/admin" option in the Remote Desktop Connection tool. You can do this by running "mstsc /v:[instance-ip] /admin" in the Run dialog.

6. If the issue persists, consider creating an AMI (Amazon Machine Image) of your instance and launching a new instance from this AMI to see if the problem is resolved.

7. As a last resort, you may need to reach out to AWS support for further assistance, especially if the problem continues after trying these solutions.

Remember that constantly rebooting the instance is not an ideal long-term solution and may indicate underlying issues that need to be addressed. It's important to identify and fix the root cause to ensure stable and reliable access to your EC2 instance.
Sources
Not able to launch EC2 instance | AWS re:Post
Troubleshoot issues connecting to your Amazon EC2 Windows instance - Amazon Elastic Compute Cloud
Free EC2 doesn't work | AWS re:Post