yiyiyorum comes from yemek. The verb stem is ye. Because it is irregular it doesnt become yiyor as it should be.

yiyiyorum : yi + y + iyor +um > verb stem + buffer + present continuous tense + personal suffix

All the souces disagree with me and show yemek as a regular verb. Winmekmak, the verb conjugator website below and most importantly TDK is suggestion "yiyor" like "yemek yiyorum". I disagree. I think the correct one should be "yemek yiyiyorum" but you might as well join the opposite as it is the majority.

http://www.tdk.org.tr/TDKSOZLUK/SOZBUL.ASP?kelime=yemek
http://www.verbix.com/webverbix/cache/31.yemek.shtml

And this is my explanation on
PRESENT CONTINUOUS TENSE SUFFIXES:

For this tense we have the following suffixes:
-ıyor
-iyor
-uyor
-üyor
-yor

The dictionary form of a verb in Turkish is the infinitive which has -mak or -mek at the end. If we drop -mak or -mek we get the verb stem or verb base. Either the verb stem is ending with a consonant or with a vowel. So we have two options. Lets start with the first:

I. If the verb stem ends with a consonant we have these options:

-ıyor
-iyor
-uyor
-üyor

You simple look at the last vowel and choose the correct suffixes. Here is the last vowel -suffix chart:

1. a > -ıyor
2. ı > -ıyor

3. e > -iyor
4. i > -iyor

5. o > -uyor
6. u > -uyor

7. ö > -üyor
8. ü > -üyor

Example:
bilmek :
-What is the verb stem?
-It is "bil".
-What is the last vowel in "bil"?
-It is "i".
-What suffix do we use for "i"?
-We use -iyor.
-So what does it become?
-It becomes "bil + iyor"


Konuşmak:
-What is the verb stem?
-It is "konuş".
-What is the last vowel in "konuş"?
-It is "u".
-What suffix do we use for "u"?
-We use -uyor.
-So what is it at the end?
- It is konuş + uyor


II. If the verb stem ends with a vowel the present continuous tense suffix is "-yor". But before you add yor check below if you have to change the last vowel or not.

If it ends with

1. a > changes to ı
yaşamak > yaşa > yaşı > yaşı + yor

2. e > changes to i
dinlemek > dinle > dinli > dinli + yor

3. ı > no change
tanımak > tanı > tanı + yor

4. i > no change
erimek > eri > eri + yor

5. o > impossible condition
No example for this. Verb stem has to end with a vowel and this vowel has to be o. I think this condition is non-existant.
We don't have o and ö after the first syllable. So it has to be a single syllabling verb stem ending with "o" which I can't think of any.

6. u > no change
korumak > koru > koru + yor

7. ö > impossible condition
Again I think non-existant. The verb stem has to end with a vowel and this vowel has to be ö. I can't think of any example. We dont have ö or o after first syllable. It could be OK if it had been in the a single syllabling verb stem but doesnt seem any.

8. ü > no change
yürümek > yürü > yürü + yor

Exercise:
demek > What is the present continous of it? Follow section II. to solve it.

There is no confusion with verb stems ending with a vowel. It is all within the rules shown above. I think there are not many exceptions. In fact I cant think of any except yemek.

The TDK is the official organisation on this subject but unfortunately not very spot on all the time. I disagree with TDK on the following words where the first is TDK's suggestion.

yiyor - yiyiyor
entelektüel - entellektüel
sağ ol - sağol
hoşÃ§a kal - hoşÃ§akal

English in its history had also some changes but these are spread to a wider time range and things are more sattled down. On the other hand Turkish had lots of changes during the last 80 years and still it continues.
In Turkish a 30 year old book can be very difficult to read depending on the author.
I also understand you on following the official suggestion but I would like take more time before doing so. They are making some suggestions and with time the daily usage may change according their suggestions. So their suggestion might have acceptance. Of course this is not always the case.