Just to be clear - is it the radio or the power that is dieing so quickly. If you were to try to use a different TX it may be difficult to find one on 27MHz that is much stronger. If you did, the modulation type would probably be different so it wouldn't work with your present RX. So now you need a TX and RX. These probably would not connect to your existing servos. This is just one of many problems encountered when buying in this price range.
No - changing antenna length will not help. In fact it could make it worse by retuning/mis-matching the circuits.

I'm sorry but you have purchased a $35 toy and this is about all you can expect. Again,sorry.