At 0.02C you battery is being considered to be fully charged, and will have already been in the CV regime since the charge current initially started to drop.
It cuts off at 0.02C to avoid leaving potential across the battery which would essentially be 'trickle charging'. In an SLA battery, this is something people do to negate the self discharge characteristics of the battery and SLAs are quite robust to it, but a LiPO or LiFePO4 in this case would be (very slowly) damaged by leaving this charging non stop (as reactions will still occur at the anode and cathode). It also increases safety as it will not be powered on and charging forever if you forget about it.
Since this is for a solar charger, what you want to do is formulate a circuit that switches the charger off when the BMS cuts off, and then switches the charge back on at say 90% capacity or some voltage less than fully charged, where the panels cannot directly handle the load thats on them. This re-initiation of the charge will allow your batteries to charge again.
An arduino could do this, and I am sure its been done many times over, but you could use it to sense the voltage of the battery and the voltage from the output of your panels. If panel output drops, under load or night, switch to battery, once battery voltage below a set value, connect charge. (I am not sure of your current setup so just speculating at this stage.
Also, if you were to be able to sacrifice some capacity for longevity. You would find that limiting charge and cutting ccharge before the BMS cuts in (somewhere between, say, 80 and 90% of fully charged), your batteries would last quite a bit longer. Depending upon you ultimate charge voltage of the BMS, this may be happening already.
EDIT: Not sure if I have mis-read your question having fully read your link. But to answer more succinctly: The main purpose of this cutoff in BMS is to stop the 'trickle charge' happening by applying a constant float potential, which will degrade your batteries. If your BMS automatically re-initiates charging as Vbatt drops, ignore my suggestion and enjoy your setup :-)