So it's first edition AD&D. You turn undead. You then attack the undead (they're cornered and can't retreat). I understand they can attack now, the turning being broken. Here is the question: Can the cleric then, as a matter of combat, turn them again over and over again?
No. The cleric only gets one attempt to try turning any particular undead.
This bit is buried in the DMG, visible in two places:
Notes below Attack Matrix III, Clerics Affecting Undead (DMG pp.75-76)
Failure to score the number shown, or greater, means the turning was unsuccessful. No further attempt can be made by the cleric with respect to the particular undead. (Emphasis mine.)
TURNING UNDEAD (DMG p. 65)
As stated on the Clerics Affecting Undead table, this function may be attempted only once by each cleric.
Yes. If you fail, you can't try again. But otherwise, you can.
The various rule mentions regarding "no further attempt can be made" immediately follows describing an unsuccessful turning attempt.
While not explicitly limiting to only failures there (e.g. by joining the two clauses like
"…the turning was unsuccessful [, and] no further attempt…"), there are other rules regarding successful turning:
From DMG 1e, p75, footnote to Turning Undead table:
Good clerics cause the creature to move directly away from his or her person, and stay as far away as possible for not less than 3 nor more than 12 rounds, moving at full speed for the duration if at all possible. The turned undead will be able to come back again, but they are subject to further turning by the cleric.
Additionally, DMG 1e, p66, Counter-Affecting:
Counter-Affecting: A cleric of opposite alignment may attempt to negate the effects of a cleric who has affected undead or other creatures. The table is consulted, and if the countering cleric is successful, the affected undead are freed of the effects of the first cleric's efforts. This counter may in turn be countered, etc. This may continue indefinitely until one or the other cleric fails and is no longer eligible to affect [that] undead et al.
The intent is clear: if you fail, you can't try again, but otherwise if for some reason the undead are once again a danger you can attempt to turn again. I would say that include situations where the (successful) turning is deliberately broken (e.g. encroaching within 10′ without opportunity to retreat, using ranged attacks, etc).