To me, my first thought when I start getting timeout errors is that it is something in the network stack.
If you are connecting to a SQL ALIAS instead of the full server\instance name, it could be a delay translating that. Might not hurtto try connecting to the full server\instance name instead of the alias and see if it helps.
It could be the server is under heavy load and cannot respond to the connect request.
Things to watch for are:
1 - does this happen at a predictable time? If so, you have a nice window to watch resources. If not, you may need to capture resource usage long term until it happens again.
2 - when it fails, are there other things running on the server? If so, maybe try spacing things out more so not as much is running at the same time.
3 - is there enough free resources to allow a new connection? I am referring to BOTH the SQL instance having enough memory (Max Memory setting) and the OS (both CPU and Memory) and the network. With the network, if, for example, you are doing a large data move on that server, you may not have bandwidth for the SQL Server. Network bandwidth is my least likely theory,but depending on how your IT team does QoS on it, you may be having some odd bottleneck there.
To me, this doesn't sound like an AD issue as it sounds like the timeouts are happening connecting to the SQL Instance; not to AD. Depending on the frequency of these, and your SQL configuration, you could try running a short term test of using a SQL account instead of an AD account for your jobs. This would rule out an AD account issue. That being said, if it was an AD issue, I would expect you could see that in the logs (either the AD log if the authentication failed or in the login event log on the server hosting SQL).
Another thing to look at would be the server logs; not just the SQL logs. The application and system logs may (likely do) have some useful things in them.
To summarize the above: check the server logs (application, system), check server resources at time of failure (CPU, memory, network), if you can, remove as many constraints as you can (AD for example) from the equation of the problem.
The above is all just my opinion on what you should do.
As with all advice you find on a random internet forum - you shouldn't blindly follow it. Always test on a test server to see if there is negative side effects before making changes to live!
I recommend you NEVER run "random code" you found online on any system you care about UNLESS you understand and can verify the code OR you don't care if the code trashes your system.