To try and clarify before you're chasing wild geese: You do not need to upgrade FML/Forge. 738 is the absolute end of the line for Forge for 1.5.2. There's nothing you can possibly "update" to there.
I know you got those parameters from your hosting company and thus they should be correct. Would MCPH be able to look on their end and see if shutdown is being forced through their Multicraft panel or if they're getting anything on their Multicraft logs on what's going on with your server? Right now what we're looking at looks basically like what you'd get from somebody with op just issuing a /stop command, which is why I ask this.
Personally, I'm skeptical that it's something in the mod pack itself versus a general resource issue being stretched because (a) I'm not seeing other reports of "it just randomly shuts off" (and believe me, we'd have them, people are not afraid to bombard us when there's an issue) and (b) I run a server with similar resource allocation (but on a dedicated box from OVH I manage personally) and with people logging in and out I haven't once had it go haywire on me (and the current instance I have up has been running continuously since 1.1.4 was released; in fact, I should probably go manually restart it just to clean the pipes). Usually, if it's something like an individual mod or interaction of mods having an issue we'd get something more descriptive attached to it and I could go "ah, yes, try X". Right after the "The state engine was in incorrect state SERVER_STOPPING and forced into state SERVER_STOPPED. Errors may have been discarded." message there should be a lot more information. If it's cleanly breaking at that point... it's highly irregular in my experience (not that I'll go to the length of saying impossible, anything's possible).
Moderator's Note: This thread is now in Tech Support, not Mod Pack Bugs. Troubleshooting and diagnosis go on in Tech Support first and if we find a definite bug then we can build a report for Mod Pack Bugs.