The administration and maintenance of Microsoft Exchange Server to ensure secure, reliable, and efficient email and collaboration services across an organization.
As I mentioned, if you are using you need to find out if you are using a load balancer.
IT sounds as if you are not. If not, you should.
If you are using DNS Round Robin, ( not recommended), then you need to talk to the DNS team if things aren't working correctly - though much of what you are describing sounds normal and it why DNS Round Robin is not recommended.
This is not an Exchange Issue per se, but really a DNS/Networking issue.
Using DNS is the simplest option for load balancing your Exchange traffic. With DNS load balancing, you only have to provide your clients with the IP address of every Mailbox server. After that, DNS round robin distributes that traffic to your Mailbox servers. The HTTP client is smart enough to connect to another server should one Exchange server fail completely.
Simplicity comes at a price, however, in this case, DNS round robin isn't truly load-balancing the traffic, because there isn't a way programmatically to make sure that each server gets a fair share of the traffic. Also, there is no service level monitoring so that when a single service fails, clients aren't automatically redirected to an available service. For example, if Outlook on the web is in failure mode, the clients see an error page.