You'll probably want to check if your server OS is able to resolve the MX:
On your server open cmd.exe (command prompt):
PS C:\Users\Administrator> nslookup
In nslookup type:
Default Server: one.one.one.one
> set type=MX
You should have an answer like this:
Server: one.one.one.one Address: 126.96.36.199
yahoo.com MX preference = 1, mail exchanger = mta5.am0.yahoodns.net
yahoo.com MX preference = 1, mail exchanger = mta6.am0.yahoodns.net
That means your OS dns configuration seems okay.
Next step would be to check the DNS configuration of SmarterMail. For this is depends the version of SmarterMail you're using.
On v16/v17 I guess it's in the general settings. If the primary/secondary dns settings are empty, SM should use your system DNS configuration.
If there are values set, you should check they are working DNS servers.
You could set them to 188.8.131.52 and 184.108.40.206 and see if the problem still occurs.
Also maybe is a good idea to check if DNS caching is enabled.
If enabled it's possible that SmarterMail keep in cache wrong DNS answers. I never really understood how the DNS cache works so I prefer to leave it disabled for safety.
Edit: Also it can be the same issue as:
Looks like If the primary DNS server is not working, SM doesn't use the second one (not tested myself though)