SELECT slows down on sixth execution

I have a very complex SELECT for which I use PREPARE and then EXECUTE.
The first five times I run "explain (analyze, buffers) execute ..." in
psql, it takes about 1s. Starting with the sixth execution, the plan
changes and execution time doubles or more. The slower plan is used from
then on. If I DEALLOCATE the prepared statement and PREPARE again, the
cycle is reset and I get five good executions again.

This behavior is utterly mystifying to me since I can see no reason for
Postgres to change its plan after an arbitrary number of executions,
especially for the worse. When I did the experiment on a development
system, Postgres was doing nothing apart from the interactively executed
statements. No data were inserted, no settings were changed and no other
clients were active in any way. Is there some threshold for five or six
executions of the same query?

Without delving into the plans themselves yet, what could possibly cause
the prepared statement to be re-planned? I have seen the same behavior
on Postgres 9.2.10 and 9.4.1.
--
Jonathan Rogers
Socialserve.com by Emphasys Software
jrogers(at)emphasys-software(dot)com