Nat – VoIP client permamently losing connection after ISP IP reset

I have a SIP client device connected to my ADSL router, so it is behind a symmetric NAT. My ISP resets the client's IP every 24 hours, it looks like this in the router log:

Mar 26 12:36:56     daemon  crit    pppd[443]: Clear IP addresses. Connection DOWN.
Mar 26 12:36:56     daemon  crit    pppd[443]: Clear IP addresses. PPP connection DOWN.
Mar 26 12:37:06     daemon  crit    pppd[443]: PPP LCP UP.
Mar 26 12:37:07     daemon  crit    pppd[443]: Received valid IP address from server. Connection UP.

Now, when this happens, my SIP client permanently loses ability to register itself at provider (I suspect it still has the old external IP cached). The only way to make it work again, is to restart the modem (or whole router), so the ADSL link is put down and up again; In other words, make this happen (router log again):

Jan 1 00:00:08  user    crit    kernel: ADSL link down
Jan 1 00:00:14  user    crit    kernel: xDSL G.994 training
Jan 1 00:00:25  user    crit    kernel: ADSL G.992 started
Jan 1 00:00:29  user    crit    kernel: ADSL G.992 channel analysis
Jan 1 00:00:36  user    crit    kernel: ADSL link up, interleaved, us=1182, ds=12444
Jan 1 00:00:37  daemon  crit    pppd[443]: PPP LCP UP.
Jan 1 00:00:47  daemon  crit    pppd[443]: PPP LCP UP.
Jan 1 00:00:47  daemon  crit    pppd[443]: Received valid IP address from server. Connection UP.

Of course I can't afford to manually put ADSL link down each time my ISP changes my IP address, just to make the VoIP phone work. So my question is, is there any way to make the SIP client work after the IP reset?

My config is:
Router: D-Link DSL-2640B
SIP Client: Gigaset A-510IP

I have already tried enabling RIP in the router, putting gigaset in DMZ, modifying the "refresh NAT time" value in gigaset config, acivating STUN… none of this helped.