From Sebastien:

Could the problem be because you cannot put more than two parts in the OR ?

FROM:
<searchType>search</searchType>
<param>
<param-name>filter</param-name>
<param-value>
(& (|(uid=%TERM%)(cn=%TERM%)(exampleEduRegId=%TERM%))(objectclass=exampleEduPerson))
</param-value>
</param>

TO:
<searchType>search</searchType>
<param>
<param-name>filter</param-name>
<param-value>
(& (|(|(uid=%TERM%)(cn=%TERM%))(exampleEduRegId=%TERM%))(objectclass=exampleEduPerson))
</param-value>
</param>