iTunes 12.1 still frequently crashes when accessing store

When I updated to iTunes 12.0.1 from iTunes 11.4, iTunes started frequently crashing on launch or if it would launch, when accessing the store. This continues with iTunes 12.1.0.71. It's crashing less often, but still does. When it doesn't crash, I frequently get messages about network connections being reset. I can sometimes get to the store, sometimes not. Trying to update Genius or iTunes Match always fails though. If I try to run the network diagnostics, it also crashes.

The above problems only happen when I'm in my office. If I'm at home or if I VPN to my home, iTunes works fine. 11.4 works fine at my office so iTunes isn't blocked by my corporate firewall, but for whatever reason 12 and up has problems.

Crash that occurs on startup, trying access iTunes account or iTunes store:

Faulting application name: iTunes.exe, version: 12.1.0.71, time stamp: 0x54c76235

Faulting module name: JavaScriptCore.dll, version: 7600.1017.6000.1, time stamp: 0x54b5da5f

Exception code: 0xc0000005

Fault offset: 0x00000000001d2121

Faulting process id: 0x24f0

Faulting application start time: 0x01d03f02b94631f8

Faulting application path: C:\Program Files\iTunes\iTunes.exe

Faulting module path: C:\Program Files\Common Files\Apple\Apple Application Support\JavaScriptCore.dll

Report Id: 0a51eba0-aaf6-11e4-8be2-f01faf3e6c79

Crash that occurs when running network diagnostics:

Faulting application name: iTunes.exe, version: 12.1.0.71, time stamp: 0x54c76235

Faulting module name: objc.dll, version: 1.528.0.126, time stamp: 0x54940801

Exception code: 0xc0000005

Fault offset: 0x0000000000020d92

Faulting process id: 0x1e2c

Faulting application start time: 0x01d03efc48783f70

Faulting application path: C:\Program Files\iTunes\iTunes.exe

Faulting module path: C:\Program Files\Common Files\Apple\Apple Application Support\objc.dll

Report Id: 9025c036-aaef-11e4-8be2-f01faf3e6c79