Verizon Razr: Text and closing phone problem

I bought a mint condition Moto Razr (Verizon) from someone about 2 weeks ago. It works perfectly and has no defects.

I had another Razr before this, but it broke. With the old one I was able to send a text message and close the phone right after I pressed "send" and it would still send the text message and say "text message send" on the outer LCD screen.

NOW, with this new phone When I press "send" and close the phone, it cancels the send of the text message. Sometimes it works, BUT most of the time it does not...

Anyone know how to fix this? I already went through all of the in-phone settings, but there is no control over this from the phone itself.