It's very common, and it's nearly always worrying. However as far as I know there hasn't been a case where any birth parent has succeeded.
What will happen is that (assuming you're in England and Wales) on the date of the first hearing, the birth parent/s will want to apply for permission to contest the making of an adoption order. They can't actually contest the making of an order unless they get permission. Providing they do manage to show up to the hearing and get some evidence together (if they come to the hearing with nothing and plead their case, they might be given a few weeks to get some evidence together and get representation if they need it)...to get the Judge's permission they will have to demonstrate a significant enough change in their circumstances. It's pretty rare for BP's to get this permission. If they don't that's the end and the adoption will be finalised.
If they do it proceeds to another hearing, and this is when they are actually contesting. This is the stage the rest of the cases fall down...no BP has 'won' at this stage, no matter how many hearings or appeals they've had (and even being allowed more than a couple of hearings is very rare). They not only have to persuade the Judge of their change in circumstances, but the childs best interests also come into play, and the childs interests are going to be served in nearly all conceivable cases by remaining with their parents where they are settled and loved, not uprooting them again.
So concerning and nerve wracking as it can be, this happens a lot and in the end it has so far never succeeded, which I hope you find reassuring. Also it only rarely gets passed the first stage, so at most normally only delays the order slightly, by a couple of weeks maybe.