We have approx 20 black berrys
When our SMTP mail server on some instances sends mails at similar times to the mobileemail.vodafone.com.fj which routes to MX=[vodafj.mx1.ap.blackberry.net] {216.9.247.34}, our sever confirms that there are "421 #4.4.5 Too many connections from your host".. Which I think is restrictions by the black berry end ?

Well I know we can limit out out going connections, but we have 20 black berry users who need to be on line and communicate at the same instance.

How can we ask hot 216.9.247.34 to accept more connections from our fixed IP ?

You will have to limit outgoing connections. There is no other way.

If you send emails to 20 blackberries it does not mean you have to open 20 connections at once to send 20 emails. Open just one connection and send emails one after another. The difference in email delivery between blackberries should not be noticeable.

In any case, it will be better than what you have now.