I either read in the book ,or on the forum, or in an e-mail from a practitioners, that energy from a session can continue to heal up to three days after a session.

That is, you might not feel a change or relief durring the session, but then the next day you may feel better, and then feel changes over the next few days as well.

Is there any rationale to thinking that the etrainment from the initial session could continue to have effect for three days?

I only ask because it seems like I'll feel improvement in my condition is excellerated for three days after a session, then the improvement plateaus.

It all depends on the individual case on how long the energy continues to work. Sometimes shorter and sometimes longer.