NOTE: please first try the steps in this article to see if it overcomes the problem: https://support.erwin.com/hc/en-us/articles/360037617271-Unable-to-start-Mart-Server-Service-after-installing-Mart-on-the-same-server-as-Data-Intelligence-Suite
There may be a port conflict. The way to tell if there is a port conflict is to start the mart server and then take a look in the catalina.2021-02-08.log file that is stored in C:\Program Files\erwin\Mart Server r9\Tomcat64\logs and see if you have a similar error:
08-Feb-2021 14:13:50.917 SEVERE [main] org.apache.catalina.core.StandardServer.await Failed to create server shutdown socket on address [localhost] and port  (base port  and offset )
java.net.BindException: Address already in use: NET_Bind
If so, you are having a port conflict and that can be alleviated by changing the port in the mart server per the above article.
Otherwise you are probably having some sort of environmental problem that is causing the mart server service to shut down. Here are some modifications that may help you to overcome that problem:
1) Try rebooting the host machine?
Please delete the mart server service. Then recreate it by right-clicking the shortcut and choosing Run As Administrator.
3) Needs a delayed startup?
Sometimes there are dependencies in windows and if those dependencies have not already started then the mart server service will not start.
Go into the properties on the mart server service
On the General tab, change the startup type to Automatic (Delayed Start)
4) Needs retries?
On the tab log on, change all the failures to Restart the Service
Apply the changes. Restart the mart server service. See if the problem continues.
If the problem continues, please also change the tab log on from Local System account to instead This Account. Choose a local user who is a member of the Windows Administrator group.