This sound extremely like a botched cabling job...
I found out that the guy that made up the cables had not crimped many of them properly and some wires were not touching the contacts etc. After fixing that...
You need to have the links measured with a proper network tester. These testers check whether attenuation, crosstalk etc. are within the allowed margins. Any link that's not been properly checked is a gamble.
A simple continuity tester just tells you whether the cables are in the right places, no shorts etc. It can't tell you if the link really works.
On the switches, check the log for up/down events and check the interface counters for any errors, especially FCS, Alignment, and Tx drops. If any of these are higher than maybe a dozen (mainly from connecting/disconnecting a link) the link is unreliable.
Additionally, if you haven't done this already: you need to set up the VLANs on the Netgear as well. The uplink trunk has to be set up in the very same way as on the Cisco. The phone ports also need to be configured as VLAN trunks.
I'm not sure if you can set up the Netgear to automatically assign phones to the VoIP VLAN. Alternatively, most vendors have DHCP options that tell phones connecting to your PC VLAN to move to the VoIP VLAN instead. You just put those on your DHCP server.