Unfortunately as /startTime & /endTime/ have been deprecated by zkill, it is no longer possible to fetch kills this way.
I believe using ESI is also no longer possible due to the recent changes.
EDIT: It's still possible to get zKB fetch working using delakut's helpful fixes from their post
I get an strange issue where it stops filling kills on the 31st of January every year. When this happens I just make sure it's pulled in everything then change the date to the 1st of February and it continues fine.
EDIT2: Noticed another issue when adding historical kills to a new board. When the amount of kills in a month is more than the limit set in "max number of kills to process per run" it will find kills up to that amount, then skip to the next month. So if you had 1000 kills in March 2014, it would find 100 and skip 900. Manually resetting the date will pull another 100 so it's necessary to keep manually going back to get all the kills.