My HTC One V was loosing connection when idle on my new router. There was no problem with the other router but due to very low signal (installed on different floor) I got a new one on my floor. Symptom was that when screen was off, phone was not responding to VoIP calls (or randomly responding), not showing notifications on new email and so on. I also found out that when doing a ping from a PC, phone was stopping to respond or responded to only 10-20% of packets when screen off.

It was weird as it worked almost perfectly with the other network, at very low signal level, as well as with the open public network in the city center. Obviously, settings for "Keep WiFi on during sleep" was set to always. I found out other people are having the same problem on the internet.

Compared router settings and finally got it... this is what I changed in advanced settings for radio part:
Preamble: short (was: long)
Beacon interval: 50 (was: 100)
DTIM: 1 (was: 10)

It solved the issue in 100%. Above settings basically improve wireless performance / timings (in theory) and for some reason phone didn't like the stock settings.

Kind regards