counting only some of the days of sefira - chatzi shiur?

The Ben Ish Chai in his Shut Rav Paalim III:32, left side of the page here brings proof from sefiras ha'omer that just like there is an issur of chatzi shiur, there is a kiyum mitzvah even if one fulfills only part of a required shiur.  

According to BH"G, sefiras ha'omer is one mitzvah that requires completing a count of 49 days.  How can a person recite a bracha on counting when there is always the possibility of missing a night and failing to complete the mitzvah?  QED, says the Ben Ish Chai, that there is a kiyum even in doing part of the mitzvah, and that kiyum is sufficient to recite a bracha on.

Halacha l'maaseh this issue comes up in cases where a person knows they will inevitably miss counting a day of sefirah for some reason.  Should they still count up until that point with a bracha, or should they skip making a bracha from the get-go knowing that they will be unable to complete the cycle?  

(An additional factor to throw into the mix in such a case is whether, if a person misses a day, we in fact view the brachos made on the previous days as brachos l'vatala or not?)

There are four separate chiddushim here in this Ben Ish Chai:

1) the assertion that chatzi shiur counts as a kiyum mitzvah, which we discussed here

2) the assertion that one can say a bracha on chatzi shiur (AH"S, among others, disagrees.  He writes 477:3 that there is a kiyum mitzvah in eating a chatzi shiur of matzah, but no bracha should be recited.)

3) the assertion that there should be a concern that one may not complete the 49 day count.

4) lastly, something bothers me about treating part of sefirah, or part of any unit of time, as a chatzi shiur, but unfortunately I can't seem to put my thumb on formulating what exactly it is that bothers me.  Maybe someone can do a better job at it.  If a person fasts half a day, for example, would you call that a chatzi shiur of a taanis?  (Maybe that's the machlokes Mechaber/Rama whether one should say aneinu at every tefilah or not, lest one fail to complete the fast?)