Why do sellers realize a penalty for repurchases soon after the original purchase?

LSX must offset administrative and remarketing costs associated with placing the fractional life settlement with a new investor, regardless of the time that has elapsed since original purchase.

Ok, I understand that, but why does the seller not receive at least some interest paid in the latter part of the projected life expectancy?

The original purchaser bought the fractional life settlement with premiums escrowed to the maximum projected life expectancy.  The new buyer will be facing "premium calls" soon (or perhaps immediately) after purchase.  If the repurchase price were more, the new investor could end up up-side-down in the transaction relatively quickly.  Reasoning:  A life settlor with a 2-4 year life expectancy 3 years later doesn't have a 1 year life expectancy; it is something more than that, (for illustration purposes) perhaps 2-3 years.  The new purchaser's price must economically reflect that and give him/her a reasonable expectation of profit.

Why would an investor sell a fractional life settlement prior to maturity? 

Change of investment timeline, financial distress, or the choice to not pay premium calls on "long" policies.