Most server based VoIP systems (i.e. Asterisk) include SNMP monitoring. Alarms and traps are generated whenever something goes awry, out of limits, or hiccups. During the 1990's, I used to do quite a bit of SNMP "instrumentation" for server farms. MRTG, RRDTool, Nagios, HP Broken View, and others were the front ends.
Sounds like monitoring nirvana? Nope... it was more like monitoring hell. No matter how I tried, I could never get the NOC to respond to alarms and traps. Nobody wanted to jump when a message popped up on the console, or wanted to slog through reams of Syslog reports looking for the culprit.
What did work was pretty pictures and graphs. Network traffic was plotted using various tools. The admins could look at the graphs and instantly tell if something had changed. Zero traffic is a good clue that the line is down. Maxed out bandwidth is a good clue that the system is under attack, or that some router was misconfigured into dumping all its traffic via that line. Lots of other possibilities, but the point is that a graph will show the past history, when things changed, and what are the gross effects.
The only people that do alarms and alerts are the burglar alarm companies.
There are IT service companies that specialize in maintaining Asterisk VoIP servers. However, you're correct that these companies don't want to deal with customer network related issues. I don't have an answer for that problem, except to find an IT service company that can do both.
For the last 30 years, my company motto has been: "If this stuff worked, you wouldn't need me". Nobody has ever disagreed.
VoIP should work out of the box, but rarely does. In my never humble opinion, VoIP configuration is the most complicated, obtuse, confusing, difficult, and buggy part of network computing. I have dealt with network sniffing, analysis, diagnostics, and performance issues that are comparatively trivial compared to the mess surrounding VoIP. Unless some industry group starts over from scratch (as they did going from ITU H.323 to SIP), it will only become more complicated and more difficult.