Making up missed prayers (For those who believe salat = prayer)

[ayyub]

I've always read on Fatwa sites that if you miss any salat (prayers) that you have to make them ALL up. Even if it is years of missed prayers. For example (from the traditional perspective of 5 daily prayers) if you haven't prayed in 10 years you would have to make up about 18,250 prayers. I recently came across this in the Qur'an which made me think about this:

19:59 Then generations came after them who lost the prayer, and followed desires. They will find their consequences.
19:60 Except for whoever repents and believes and does good work; they will be admitted to Paradise, and they will not be wronged in the least.

So in the first ayat it talks about people who stopped praying, followed their own desires and thus will face the consequences of their actions. The second ayat says except whoever repents, believes and does good work. So wouldn't that mean if you stopped praying and you repented, increased your faith and started doing good works you would be forgiven by God? Am I missing something here? 

[Wakas]

In 19:59 it compares and contrasts "neglected/wasted the salat" with "following the lust/desires". In Quran, following lusts/desires is always in opposition to following God's guidance, and of course following God's guidance means acting out what it says, so this is naturally connected to good deeds.

[Jafar]

Another evidence to support salat = commandment.
If you missed God's commandment (by doing bad deed, murder, lying, tricked other people for your own selfish benefit, dishonest etc..)
You need to repent and amend your bad deed with a good one.