The only installed BCM50 cartridge (BCM 50 R2 Element Manager Cartridge 3.0.0) would indicate that this is a BCM50 R2 system. BCM50 supports maximum of 32 IP phones in the normal mode or up to 80 IP phones in the SRG mode. I am pretty much sure you're not using SRG, so you are limited to 32 IP phones. Based on the information that there are about 60 phones on the system, you either have all digital or a combination of digital and IP phones.
In any case, using BCM50 for 60 users - for example 32 IP phones + 28 digital phones (base + DSM16 MBM) + 23/30 digital trunks (DTM MBM) - is certainly pushing the BCM50 system to its limits. If you get close to 30 calls from IP phones to PSTN combined with several users accesssing voicemail, the BCM50 is likely running at 100% CPU.
You could use BCM Monitor to monitor the system's activity - either to watch it while these problems occur or you can enable logging to collect data that you can analyze later. In BCM Monitor, you can see the memory and CPU usage, number of active calls, utilization of lines, etc.
The problem description - users cannot hear callers - does not include information for how long they have no voice path. If it's just a brief period of time, maybe it could be caused by the voicemail component. Check if there are some mailboxes with a (very) large number of messages - if you find any, clean them up. From what I remember from R1/R2 days, mailboxes with many messages could cause voice path interruptions ranging from a few hundred milliseconds to several seconds (depending on the number of messages) for calls between IP and digital (IP phones over digital trunks or digital phones over IP trunks). There was no impact on digital to digital calls (digital phones over digital trunks).
If at some point you get to contemplate a more radical solution - whether to get further expansion capacity or for performace reasons - an upgrade to the E-MetroTel's UCx system might be worth consideration. With the UCx system, you would keep all the phones (both digital and IP), from the user perspective phones would behave pretty much the same way, but all call processing and advanced features would be handled by the UCx server. Plus you could add more Nortel phones, SIP trunks, SIP phones...