I want to leave a reference for people who may find this, as the linked question actually asks for something else (even if one of the answers contains the solution to this problem).
The key binding to move forward is CTRLS.
The problem is that this binding, in many terminals, is used by default to send the pause transmission code (XOF).
As in man stty:
[-]ixon
enable XON/XOFF flow control
So, if you have this option enabled on your terminal (the output of stty -a contains ixon withouth the - sign in front), you cannot use CTRLS in the context of reverse-i-search.
To disable it, use the following command:
stty -ixon
And CTRLS will give you a (i-search) (non reverse).
