The question may be misleading, so I'd like to get some clarification;
Two servers, each running 1 DNS resolver - but are each server containing a copy of the client's site? Meaning files & databases are setup on two separate servers? (possibly setup on 1 server and then rSYNC to a second machine?)
If so, then as answered by others, you would need to suspend the account on both machines.
If you're using two servers to operate the DNS, and they're configured to act as a cluster, then the DNS points the user to the right place and it's the end server (client account) that controls if things are suspended or active.
DNS can be tricky at times and depends on how things are configured.
There are occasions where nameserver records are looked up using a random order, or in some cases they may even be queried in parallel and the first to respond is the one it resolves to. This avoids overloading of a single server. We used a variation of this years ago. You can see more at the Wikipedia article about the positives and negatives of such an implementation -
https://en.wikipedia.org/wiki/Round-robin_DNS
So I guess a little more clarification on how you've configured your DNS and what you mean by the account being active on one and suspended on another (appearing as two separate end points).
