Let's start my making the query readable:
SELECT a.referenceid, a.memberid AS d1, b.memberid AS d2, c.memberid AS d3, d.memberid AS d4, e.memberid AS d5, f.memberid AS d6
FROM jos_comprofiler_members AS a FORCE INDEX (aprm)
LEFT JOIN jos_comprofiler_members AS b FORCE INDEX (aprm) ON a.memberid=b.referenceid AND b.accepted=1 AND b.pending=0
LEFT JOIN jos_comprofiler_members AS c FORCE INDEX (aprm) ON b.memberid=c.referenceid AND c.accepted=1 AND c.pending=0
LEFT JOIN jos_comprofiler_members AS d FORCE INDEX (pamr) ON c.memberid=d.referenceid AND d.accepted=1 AND d.pending=0
LEFT JOIN jos_comprofiler_members AS e FORCE INDEX (pamr) ON d.memberid=e.referenceid AND e.accepted=1 AND e.pending=0
LEFT JOIN jos_comprofiler_members AS f FORCE INDEX (pamr) ON e.memberid=f.referenceid AND f.accepted=1 AND f.pending=0
WHERE a.referenceid = 1593 AND a.accepted=1 AND a.pending=0 AND f.memberid = 1593
AND b.memberid NOT IN ( 1593,a.memberid)
AND c.memberid NOT IN ( 1593,a.memberid,b.memberid)
AND d.memberid NOT IN ( 1593,a.memberid,b.memberid,c.memberid)
AND e.memberid NOT IN ( 1593,a.memberid,b.memberid,c.memberid,d.memberid)
AND f.memberid NOT IN ( 1593,a.memberid,b.memberid,c.memberid,d.memberid,e.memberid)
LIMIT 0, 1
Okay... for starters, you may *THINK* you have a series of LEFT JOINs there, but in fact because of your WHERE clause you have converted EVERY ONE OF THEM into an INNER JOIN!
You will have to decide if you NEED those to be LEFT JOINs, so that you will then rewrite all the ON conditions, or if INNER JOINs are adequate.
And then you need to use MySQL's EXPLAIN
to see what it says it is going to do.
You also have at least one self-contradictory condition in there. To wit:
WHERE ... AND f.memberid = 1593 ...
AND f.memberid NOT IN ( 1593, ... )
You have, effectively, said "never select a record from table f".
Finally, I don't see how we can guess how to help you when you don't show the definitions of your two forced indexes.