Where GTM gives a flexibility moving your traffic back and forth between multiple Data Center or removing a particular DC in and out of rotation on the fly, It comes with certain limitation. GTM is a DNS based load balancing system. The drawback of DNS based system is, it only talks with Name Servers.
In normal request/response cycle, A User hits its ISP's Name server and GTM distributes the request on basis of the User's Name servers. Now think about 100 user using the services of same ISP and let's say GTM handed out your DC's IP with TTL of 60s. For next 60s GTM will not get hit from ISP's Name server again. In that 60s, these 100 users may send 100 request or 1k request which GTM is not aware of hence GTM can't distribute the traffic on basis of end user's http traffic. GTM has no idea of the actual user IP addresses on behalf of whom the client caching nameservers are acting. Moreover, GTM cannot keep track of what answers it has given in the past per nameserver, as there are too many client caching nameservers for that to be practical.
One consequence of this is that it is impossible to guarantee stickiness. Data center affinity and persistent assignment can improve the chances of keeping a user mapped to the same server over time, so as to preserve things like server-side session state, but can not guarantee, stickiness.
In case you have any question or concern, You can reach out to Akamai Customer Care.