From the 1955-1956 AMA rulebook:

18.  CONTROL LINE COMBAT REGULATIONS

..........


18.4 NUMBER AND TYPE OF MODELS. Each contestant shall be permitted a maximum of two
       models in this event, but only one of these models may be used in any one flight. To
       be eligible for enry, each model must be capable of attack and evasive maneuvers and
       have no intentional sharp protuberances or devices for the purpose of cutting streamers.


..........

18.6 NUMBER OF FLIGHTS. Each contestant will be allowed two attempts for official flights.
       Unofficial flights described below will not be scored as an attempt and contestant shall
       be allowed an additional attempt.


The matching and scoring were similar to the East Coast Formula GX and the points for both
flights were totaled.  There was also descriptions of calling more than two contestants to
the circle and the first two airborne flew the match, while the others were not charged with
an attempt or an unofficial flight.

It then goes on to describe another type of event:

ELIMINATION COMBAT

18.16 If the contest time and facilities are adequate to allow all contestants to compete
        in the event, the Contest Director may elect to hold an "Elimination Combat Contest".
        All combat rules and procedures previously listed shall pertain to this event except
        where changes are noted below.

18.17 NUMBER OF MODELS.  One model shall be allowed for each official flight flown.

18.18 NUMBER OF FLIGHTS.  Each contestant will be allowed one attempt for completion of
        one official flight plus whatever additional flights are required to complete the
        elimination order.

18.19 SCORING.  "Cut" and "Kill"  points will be used only to determine the winner of each
        match and will not be accumulated.   .....  (Further description of elimination and
        number of rounds)


It seems to me this means that you can use more than two models in "Elimination Combat".

So, to answer the original question, it seems that there were two types of combat and
one had a two model limit, while the other did not.  

Now I know why the Flying Eagles had everybody and his brother working on Hap Wakefields plane after a match.  This was at my first control line contest in Stanley KS.   A little airfield west of town.   Dad set and watched the combat until the end.