I've got 2 ASA5505's configured as easyVPN clients connecting to Cable ISP. The ASA will initially get an IP but when it tries to renew the ISP's DHCP server responds from an private IP which is ignored by the ASA as it did not from the IP to which the renewal request was sent.
ASA gets 24.X.X.X from 184.108.40.206 (ISP DHCP lease server)
When the renewal counter expired the ASA sends a request to renew to 220.127.116.11
the ASA receives a DHCP ack from 10.70.0.1 which is ignored "not for us"
so eventually after the 4 retry counts for both renew and rebind expire the ASA drops the tunnel and rebroadcasts for an IP.
I've experienced this with 2 separate ISP's