Looks like it's certainly an issue for others too. I'm just surprised it's not more prevalent; I guess not many people use a VPN on their phone?
Due to a bug in Android 4.4 (KitKat) reported to Google under Issue #61948, AnyConnect users will experience High Packet Loss over their VPN connection (users will experience timeouts when attempting to access certain network resources). In the ASA logs, a syslog message will appear with text similar to "Transmitting large packet 1420 (threshold 1405)."
This has been reported to Google under Issue #61948
Android 4.4 TCP advertises incorrect MSS over VPN (using VpnService)
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Android 4.4 (KitKat) including the Google Nexus 5
Until Google produces a fix for Android 4.4, VPN administrators may temporarily reduce the maximum segment size for TCP connections on the ASA with the configuration command "sysopt connection tcpmss <mss size>". The default for this parameter is 1380 bytes. Reduce this value by the difference between the values seen in the ASA logs. In the above example, the difference is 15 bytes; the value should thus be no more than 1365. Reducing this value will negatively impact performance for connected VPN users where large packets are transmitted.