it s complicated and too many factors are in place to give 1 answer for you.
no point in refreshing [by refreshing I understand recasting a spell that is currently still affecting the target] a dot that is not enhanced by current eclipse (in your example you re about to leave lunar, so no point to refresh sunfire if it s still on the target).
you should keep as many dots on as many targets as possible in order to get shooting stars proc, that allow you to cast instant starsurge.
in multitarget situation you should multidot them using the dot (SF or MF) right for the current eclipse that you re in, and not waste GCD for casting the dots that are not eclipsed, so in solar eclipse you multi sunfire, in lunar you multi moonfire, (unless it s less than 4 targets, when it makes sense to apply eclipsed dots first, and then if you have time - the noneclipsed ones). by "if you have time" I mean if you dont have an SS procs (or chain SS procs) to cast.
in single target situation I find it best to refresh the right dot when you re getting into the eclipse, otherwise I only recast the dot when it expired.
in case you re not in eclipse when multidotting becomes possible you should get to the eclipse fast; to do that you have a choice to either
cast dots uneclipsed hoping for quick SS proc, to get you to eclipse fast, or
keep on casting wraths/starfires until eclipse, or
maybe (the worst idea in my opinion) even use astral communion.
I've been wondering this aswell. Some people say that you shouldn't need to apply dots more than 1 time per cycle (from Lunar eclipse to Solar Eclipse etc). Currently I'm applying dots once I get into eclipse(non-eclipsed dot first and then eclipsed dot for the initial dmg increase that lunar shower brings) , but I can't seem to get to the other eclipse fast enough! Is it better to just let them fall off and then reapply them once I've reached the new eclipse?
This is not a very easy question, because it is dependant on more then just eclipse state. It also depends on if nature's grace is still up, do you happen to have spellpower or intellect procs running or not, jade spirit procced or not? All those things up in the beginning of a cycle and you apply dots may be worth not to refresh dots at the end of a cycle if they dont have that bonus, it is worth it to have the dots drop off for a second. Also it depends if you foresee movement or not, if you know you can stand and spam you prob dont need to refresh dots before going out, cause you can make it to next eclipse. If you have to move in between, then refresh.
Tip get many poweraura's, weaksaura's to track buffs and procs
if you re able to track your proccs (trinkets enchants and abilities) and you can remember if your dot on given target was cast under the proc
then you can consciously decide whether or not to refresh the dot.
in multi target situation this is close to impossible though , unless you re a hardcore that spend 5 hours a day mastering it :P
being casual (like me) in multitarget you just spam tab MF or tab SF,
in single target fights this is much easier to see (and remember) when your dot is buffed by a procs, and then it s easier to decide if you should refresh it or let it expire and then recast it (perhaps waiting a sec or two for getting into eclipse before reapplying it)
I was under the understanding that upon entering your eclipse you refresh dots and right before you leave the eclipse you refresh dots. That way as you leave the eclipse and pushing to the next one you are still benefiting from the empowered dots of your last eclipse before you have to refresh them 15 seconds later.
But like was said above, they maybe not be worth refreshing if a SP trinket proc'd or if NG was up as the old dots would be more powerful and thus tick for higher damage then if you were to refresh them at the end of the eclipse without the SP trinket/NG running.
I've been kind of going back and forth on this as well. Right now I'm tending towards refreshing dots before leaving eclipse under the assumption that movement is going to slow down my entry into the next eclipse, unless I have an SS proc ready that will push me there faster. I'm still feeling pretty awkward about not having this down perfectly. :-P