The problem is in the receiver and the only way to reduce it is to change the transmitted data to make it easier to find at the receiver. The receiver is running all the time and its output depends on the amplitude of the signal it receives. Unfortunately, when there is no transmission at all, they produce random output. The problem with ASK (or OOK) transmission is it sends a signal out when a logic high is sent to it and nothing out when a logic low is sent to it. So as far as the receiver is concerned, it either sees logic high or random data, not much use when you can't tell the 0's from the 1's.
There are some tricks you can use to improve reliability, the first is to send a transmission for say 200mS before sending the data itself. You can do this by making the data input high for 200mS, forcing the transmitter to send it's signal. This gives the receiver a chance to adapt to the signal level and 'quieten down' before the real data arrives.
You can also add a low-pass filter at the data output to help remove pulses shorter than a single data bit.
After that, the only method is to pre-condition the data before transmitting it to make it more recognizable at the receiver, possibly adding error correction bits to it or an automatic resend protocol.
FM is far better in almost every way and only cost a fraction more. The NRF24L01 mentioned by Easyrider83 is cheap and easily available. It has the advantage of doing all the processing to improve reliability, using FM and also having an automatic check and resend function built in to it. The downside it it needs some preparation data to configure it before use.
Brian.