EMAIL's are not being received by recipient -

I am having an issue with sending emails - and its happening on 2 out of the 4 email accounts that I have. I am able to receive an email but not send to  recipient .  I tried sending to both GMAIL and other servers.  No Luck

Nothing is bouncing back and it seems that the message is sent an I can see it in the send box but its not being sent.  Is there something with the SMTP send server - maybe something has changed?  Oddly , it seems that the message is sent.

Thanks in advance for you help.  I see this is an issue that is faced by others too so please let me know if any one has any hints on how to fix this as this is a business account and its hard to run a business if this happens

Thanks