It does not work in UDP mode, if your SIP server can be switched to TCP mode it should work (eg: for asterisk use transport=tcp in your sip.conf). It seems that IOS does not allow UDP traffic in background mode.
I recommend you to switch to SIP TCP/TLS for having background mode working on Linphone for IOS.
The only way to workaround this UDP problem is to force the iphone to stay live by creating a long running background task. The result is that the device never suspends, which drains the battery very fast.