Hong Kong offers Kenyans, and many other nationalities, visa-free, 90 day entry permits.

Similarly, Thailand offers many other nationalities, visa-free, 30 day entry permits.

To put a stop to abuse of their visa-free entry system (long-term stayers simply crossing the Thai border, in and out, every 30 days), Thailand introduced a limit of 3 visa-free entries for any 6 month period. Visits with an actual visa were unaffected.

I suspect that Hong Kong has a similar system - a limit to the number of times a person can enter Hong Kong during a specified period, unless an actual visa has been obtained.

I further suspect that your predecessor had probably been visa-hopping for sometime; traveling from the mainland to Hong Kong every 30 / 60 days to get new L / F visas for China.

The reason I suspect such is because I've heard many, many reports that the authorities in Guangdong will not longer issue paperwork necessary for English Teacher job applicants to obtain a Z visa to anyone who is not from the US, the UK, Canada, Australia or New Zealand.