Problem with email receiving and probably sending

Problem with email receiving and probably sending

we face a big problem with incoming emails.

All emails are either delayed -a lot- or lost.

I noticed that emails sent from our domain to our domain (inside the organisation) are delivered, but others from outside
are not.
Our domain is : giannopoulos.gr

I am very curious, why is this happening, and if this happens often - as we are new users.

We are very satisfied with the services provided here, but when its about business emails, consistency is No.1 priority.
I suspect that all the emails in between are LOST??

I am bit sceptical about the stability of this platform and although i can accept small delays, i could not live with lost emails.

Thank you all.

Regards,
George.