The damage cap varies from generation to generation.  So, until you establish (or are informed) what the damage cap is, you won't be able to optimize the damage inflicted in a session.  For Generation 724, the damage cap was very close to what is often referred to as a two dot span.  This is the span covered by three dots.  The distance between the first and second dot is a one dot span and the distance between the second and thrid dots adds another dot's span for a total of a two dot span length.

I normally discover the damage cap by trial and error rather by a systematic approach to discover what it is.  Below are two videos that demonstrate the damage cap for Generation 724.  The first exceeds the cap and the second that does just a little less damage than the first is under the cap:

An Ur-D Session just exceeding the damage cap. The server is not accessed following the fight10:39

An Ur-D Session just exceeding the damage cap. The server is not accessed following the fight.

I had not been intending to exceed the damage cap in the above video.  However, Nei who had been set up as a Ranger with a preference towards shooting decided to climb instead.  This intensified the damage.  Though I tried to regulate it by switching from 100 Kisses to a Light attack late in the fight, the server was not accessed when Ur-D retreated indicating the damage cap had been exceeded.

Contrast the above video to the one below.  It is from the same generation but earlier in the cycle.   As in the above video, Nei grapples and uses 100 Kisses intensifying damage inflicted.  However, I do a better job in holding back and the damage cap is not exceeded.

Even with the same party and the same tactical approach to fighting the Ur-Dragon, damage inflicted can vary radically.  Not only do the Ur-D's hearts contain different levels of health but the pawns may vary their approaches.  In the below video, Nei who had been attacking at range with the bow, at 2:43 jumps on the Ur-D's rear left thigh.  

At the onset of the fight, the Ur-D's health bar was just above the seventh dot.  The damage cap would thus be exceeded if the health bar moved beyond the fifth dot--a distance equivalent to that in the above video.   It is clear very early on that the rate of damage will exceed the cap at the current rate of damage.  Leila switches from 100 Kisses to normal light attacks to slow down the rate of damage.

The Ur-Dragon leaves a little early.  His health bar is just about at the 5th dot.  Had the Ur-D not left early, the damage cap would have been exceeded and the round would not have counted.

Managing the Damage Cap07:51

Managing the Damage Cap

One can prevent exceeding the damage cap by departing early.  However, if you depart before the Ur-Dragon retreats, the round will not count in the statistics tracking the number of times the Ur-D has been repelled.  So, an alternative is to gather the party and retire to a location in the chamber where you will not engage the Ur-Dragon.  In this manner, you can get credit both for the damage inflicted as well as repelling the Ur-D.