Looking at the code, the point where the individual ArenaEnemyFrame items are being modified is when "ArenaEnemyFrame_UpdatePlayer" gets called.
Move the lines that clear and set the points for the ArenaEnemyFrame 1 through 5 into its own function. Have the code run that on load, and then use hooksecurefunc to have that function run when ArenaEnemyFrame_UpdatePlayer" runs.
I have not tested this code, but...
Code:
function relocateArenaEnemyFrames()
ArenaEnemyFrame1:ClearAllPoints();
ArenaEnemyFrame2:ClearAllPoints();
ArenaEnemyFrame3:ClearAllPoints();
ArenaEnemyFrame4:ClearAllPoints();
ArenaEnemyFrame5:ClearAllPoints();
ArenaEnemyFrame1:SetPoint("CENTER",UIParent,"CENTER",343,44);
ArenaEnemyFrame2:SetPoint("CENTER",UIParent,"CENTER",343,18);
ArenaEnemyFrame3:SetPoint("CENTER",UIParent,"CENTER",343,-8);
ArenaEnemyFrame4:SetPoint("CENTER",UIParent,"CENTER",343,-34);
ArenaEnemyFrame5:SetPoint("CENTER",UIParent,"CENTER",343,-60);
end
hooksecurefunc("ArenaEnemyFrame_UpdatePlayer", relocateArenaEnemyFrames);