The MX DNS is a forwarder. If you point clients to use the MX as the internal DNS, it'll forward those requests to the DNS you have set on your WAN interface, unless you specify something else in the DHCP configuration.
Do you have a separate DNS server? Where is that server configured to forward DNS requests? If they all go to the telco DNS and if they're having an issue, connections will drop once the TTL of the domain name expires. For example, office365.com has a TTL of 5 minutes.
Where does your internal DNS server forward requests? It doesn't matter if clients are querying an internal DNS server if it is not authoritative for that zone, it will still forward the DNS lookup once the TTL of the A record expires.