In the month of Ramadan, what should a person who couldn't wake up for suhoor do? Should he continue the fast or should he compensate for it later?
Eating Suhur is Sunnah. Not obligatory. As Prophet Muhammad (Salla-Allahu-Alaihi-Wa-Sallam) Says,
But, Keeping Fast during Ramadan is Obligatory for every Muslim. As described in the Quran and many Ahadith of Prophet (Salla-Allahu-Alaihi-Wa-Sallam).
The Ayat from Quran is
So, the conclusion is, Even if you missed Suhur, You have to fast. Suhur is not obligatory and it is a Sunnah and Prophet says, there is Barakah (blessings) in Suhur. But, it is not in the per-requisites of Fasting
Hope this will help
All the other answers (correctly) point out that fasting is wajib (obligatory) and suhoor is sunnah (in the sense that it is not obligatory, but recommended). However, more clearly, the reason you still have to fast is because of the conditions of fasting:
As you can see, suhoor is not a condition for fasting - and therefore you are obliged to fast despite missing suhoor. If one of the conditions is broken, only then you are not obliged to fast.
So while the wajib/sunnah distinction is valid, technically it would be that suhoor is not a condition for fasting that gives you the answer to your query. And Allah knows better.
You can and you must!
There is no excuse of breaking the fast if you skipped Sehri for one reason or another. Sehri (mid night meal) has it own benefit and is recommended by the prophet but that is not a requirement for fast. All you need to do is make your intentions for fast and offer prayer. The prayer is
'Wa be somi ghadin navaithu min sheri ramadan' meaning
" I have made the intention of obligatory fast for this day of Ramadan for the sole pleasure of Allah Almighty."
So in short sehri is not compulsory for fasting but it is highly recommended. If you skip it which can very well happen, you should still keep the fast.
If you skipped sehri and now it is too hard for you to keep the fast, that is probably another question.
As othe answers mentioned, suhoor is a Sunnah (and a recommened Sunnah), but it's not obligatory, and many people don't take it when the fast-time is short and the eating-time is long, however it's still recommended to take it, as this Hadith mentions:
So you see that suhoor is a confirmed sunnah, but it's still Sunnah, not obligatory, not taking suhur:
As you see Quran explicitly says that you can eat till fajr time, and after that you'll have to fast until Maghrib.
Hope that's helpful.
Of course you should fast even if you miss suhoor. Kids above 12 years must fast. Anybody younger who couldn't take hunger don't have to fast. But when they do suhoor they should fast.
Suhoor is a Sunah. You must fast if you eat at that time. Fasting is mendatory for anybody at a puberty age (12+ years).
So even though you miss suhoor, if your 12+ years, you must fast at all costs.