Now I get it! It’s really hard. I just got my first practice set. I literally felt like I was wrestling the bag and bellows. I was able to play 2 half notes, a low d and e, then the bag ran out of air. Then I played a couple of eigth notes, and the bag ran out of air. I assume you keep the bellows closed while you are pushing the bag. How do you keep the air going for a whole tune? 
Don’t try to play tunes at first. Just hold a note and practice keeping the bag inflated. As you pump in with the bellows, ease up proportionally on the bag, then slowly increase pressure on the bag as you re-inflate the bellows. Keep pumping with slow even strokes. Do not try to pump the bellows in rhythm with a tune. The bellows must be independant of anything else you do. Do not jerk or slam the bellows closed. Slow, smooth and steady. Do not try to play the chanter with the bellows. Use the bellows to inflate the bag. Use the bag to play the chanter.
Practise just bellows. You have to get the bellows operation down to the point of an unconscious habit. Once you can keep one note going steady, regardless of what stage you are at with the bellows, then you can try a few notes. Get Heather Clarke’s Uilleann Pipes tutor.
djm
Perhaps thinking of it in terms of blowing your arm off the bag… but lightly so. Eventually the rhythm will come and soon you’ll be amazing yourself.
djm suggests trying to maintain a single, steady note while operating the bellows, he also suggests the Heather Clarke tutor… djm is mad, MAD I tell you… but he is also correct (IMHO). 
You made notes? Musical notes? If I could do that the RSPCA would leave me alone!
There is a flap valve in the bellows to bag connecting pipe. If that is not functioning or has been put in upside down it will allow precious bag air to get out back to the bellows. The only way for the bag air to go should be down the chanter.
Keep the bellows going at a regular pace.
Welcome to the boards and best wishes.
I learned the bag/bellows thing by taking a cork and boring a hole in it that took about as much air as when sounding the reed.
Plug the cork into the chanter stock and learn the place where “one gulp” of the bellows “almost” tops off what the bag will hold.
As you approach the bag deflation, take the biggest gulp of air with the bellows and slowly pump the bag full while keeping the same pressrue as you were holding before you started pumping the air over.
Are you confused, yet?
Make sure you don’t have any leaks… You should be able to air up the bag and blast off many notes without even touching the bellows…
eedbjp,
I’ll assume you have bought from a reputable maker and the pipes have been checked over before they were sent to you.
Basically, the pipes are not hard work (although as a beginner you may not believe that) and it all boils down to technique. However, if there are any leaks then you will really struggle. The earlier replies point you in the right direction should you suspect any loss of air.
I was several weeks before I could play two full octaves when I started out and my initial thoughts were “…their must be something wrong with these pipes”. Not so of course and it was me.
Just practice filling the bag with air and with the chanter unplugged and only allow a small but steady flow of air out of the bag with your finger until you can get the rythm of bellows control. That in itself will not take long to master. Once you feel comfortable with the bellows move back to the chanter and aim for steady sustained notes using bag pressure not bellows pressure.
You will soon be in a position where bag and bellows require little in the way of “concentration” and it will become automatic.
Don’t worry, we’ve all been there. Just keep practicing.
Finally, if you have any doubts about leakage or a very tough reed then you will need to seek out another piper (at intermediate level possibly) and ask for a second opinion.
Good luck and welcome to the bad, mad world of Uilleann piping
Joseph (the UK one) 
It turned out to be the flap valve. I sent it back to the maker and he’s taking care of it. Thanks for your help. Brian