At times when ISP drops an internet connection, it is needed to put the router in bridge mode so that the public ip address can be directly assigned on the inside firewall (any brand).

So you can put a cisco router in bridge mode this way;

bridge 1 protocol ieee

int fa0/0   <–connected to ISP (change interface accordingly)
no ip address
bridge-group 1

int fa0/1  <–connected to ASA (change interface accordingly)
no ip address
bridge-group 1