The amendment to Article 23 of the Enforcement Rules of the Labor Standards Act was passed on Dec 9 and will come into effect on Jan 1, 2016, along with a few other changes. The total holiday count will drop from 19 to 12 days. The MOL still says it's justified by the extra days off created by the 40 hour work week, though obviously that only applies to (some) full-time workers. Here's the official announcement: mol.gov.tw/announcement/2099/24365/
And here's the relevant text of the LSA ER:
Art. 23-1 requires a substitute holiday if a holiday falls on your LSA Art. 36 day off (not necessarily the weekend) or on a day off that results from the amendment of LSA Art. 30 (the 40 hour work week).
Art. 24-1 clarifies, redundantly I think, that "休假" in LSA Art. 39 refers to both the holidays referred to by LSA Art. 37 (i.e. LSA ER Art. 23 as above) and the annual ("special") leave referred to by LSA Art. 38.
The LSA was also amended this month, though not the articles involving holidays etc. New translations are not available yet, so I'll take the liberty of listing the holidays for 2016 in English.
一、中華民國開國紀念日：一月一日。Jan 1, ROC Founding Day
二、和平紀念日：二月二十八日。 Feb 28, Peace Memorial (2-28) Day
三、國慶日：十月十日。Oct 10, National Day
本法第三十七條所稱勞動節日，指五月一日勞動節。May 1, Labor Day
一、春節：農曆一月一日至一月三日。First three days of CNY
但逢星期四時，於後一日放假。Apr 4, Children's Day, or Apr 3 if it falls on the same day as Tomb Sweeping Festival, or Apr 5 if it falls on a Thursday
三、民族掃墓節：定於清明日。Tomb Sweeping Festival / Qingming
四、端午節：農曆五月五日。Dragon Boat Festival
六、農曆除夕：農曆十二月之末日。Day before CNY
七、其他經中央主管機關指定者。(MOL can designate additional holidays by decree)
So that means Jan 2 (day after ROC Founding Day), Mar 29 (Revolutionary Martyrs Day), Sep 28 (Confucius Day), Oct 25 (Taiwan Restoration Day), Oct 31 (CKS Day), Nov 12 (SYS Day), and Dec 25 (Constitution Day) are out. Of course, if you're confused because you never got those days off in the first place, it's probably because your boss ripped you off, but there may be a holiday swap clause in your contract etc. If you ask the Ministry of Labor or your local labor department for a clarification, be sure to specify which year you're inquiring about.