Corpus luteum during the luteal phase and gonadotropins
Lots of questions, so I'll break them down one at a time:


  Does the corpus luteum operate independently of the hypothalamic-hypophyseal-ovarian axis? 



The corpus luteum does depend on intact pituitary signalling.  Hypophysectomy at the beginning of lutenization will result in cessation of corpus luteal growth and subsequent drop in progesterone; in essence, the corpus luteum won't grow and function properly in the absence of pituitary hormones.  In some species, estradiol is needed, so intact gonadal steroidogenesis is also required.



  In an ovarian cycle where there is no pregnancy, do FSH and LH affect the corpus luteum? 



Elaborating on the above, yes pulsatile secretion of LH is required to fully develop and maintain the corpus luteum (not so much for FSH).  Other pituitary hormones, such as growth hormone are also involved.  In pregnancy (or pharmacologically), a large dose of hCG can sustain the corpus luteum.  hCG and LH are homologous.  Depending on the species, prolactin and estradiol are also required.



  Is it true that the corpus luteum degenerates because of low FSH and LH levels? 



The corpus luteum degenerates (luteolysis) because of prostaglandin produced by the uterus.  In the absence of a uterus (and therefore prostaglandin), luteolysis is delayed.  It is reported that estradiol from the next batch of follicles triggers oxytocin release by the posterior pituitary and subsequent release of prostaglandin and thus is the penultimate cause of luteolysis.



  Why doesn’t the corpus luteum degenerate immediately after the LH surge, then, whereafter FSH and LH levels are so low? 



As described above, it is not low FSH and LH that cause luteolysis.



  If not, then why does the corpus luteum degenerate?



Described above.


Source: http://physrev.physiology.org/content/80/1/1.long