PDQ and Modem devices will struggle to work on an ATA device except for brief 9,600 baud connections. SIP is not a reliably clocked protocol, so frame-slippage occurs in the translation from analogue to SIP to ISDN and means it is generally very unreliable except for short transmissions.
If the communication is over the Internet, there is virtually no chance that it will work as the jitter introduced as the data crosses the Internet is variable.
For extended PDQ and Modem usage, we suggest connecting them to a real analogue line. The vast majority of services where PDQ/Modem equipment is used are replacing these devices with online equivalents, which will eventually make the problem disappear.