it's a JSF thing
you could add id's to all your JSF naming containers (h:form, etc.): then the id would not change dynamically, or you could use smth. like the j4j:idProxy

Depending on what you are doing you could also probably make use of rich:jquery or rich:componentControl. 

You have multiple possibilities

If you are using a4j on your page then you can use prototype.js (rendered by richfaces) - in the newest richfaces release prototype.js 1.6 is used.

<h:form id="myForm">
....
<h:inputText id="myControl" .....

</h:form>

is rendered like that or something similar ...

<form id="myForm">
 .... 
<input id="myForm:j145:myControl"
</form>

you can find that control with the following javascript

<script>
  var cometome = $('myForm').select('input[id$=:myControl]'); // matches the end
  alert(cometome);
  var cometome2 = $('myForm').select('input[id^=myControl:]'); // matches the beginning
  alert(cometome2);
  var cometome3 = $('myForm').select('input[id*=:myControl:]'); // matches any part of the value
  alert(cometome3);
</stript

or you put a cssclass on your input

<h:form id="myForm">
 .... 
<h:inputText styleClass="findMe someOtherClass" ...

and find it by doing this

<script>
 var cometome = $('myForm').getElementsByClassName('findMe');
 // you receive an array
 alert(cometome[0]);
</script>