There has been some very good advice given here on this question. But, if
there are no bad sockets or connections, and if the bulbs themselves aren't
defective, then I think the simple solution to this problem is to simply
install a very simple, low-cost booster transformer at the end of the line
(or at the point where the voltage gets too low). See the link with the
attachment. These small transformers are used when the voltage drop is too
low at the end of a 12 volt line. If the voltage is say, 9 volts at the
end of the line, this unit will boost it back up to 12 volts.

I am quite sure that Intermatic makes these as well.

James