@Brad: Your answer isn't complete; he's most likely doing it too late in the page lifecycle, during the Page_Load event.
Okay, here's what you're missing.
ASP.NET is stateless. That means, after your page is rendered and sent to the browser, the page object and everything on it is destroyed. There is no link that remains on the server between that page and what is on the user's browser.
When the user clicks a button, that event is sent back to the server, along with other information, like the hidden viewstate field.
On the server side, ASP.NET determines what page handles the request, and rebuilds the page from scratch. New instances of server controls are created and linked together according to the .aspx page. Once it is reassembled, the postback data is evaluated. The viewstate is used to populate controls, and events are fired.
This all happens in a specific order, called the Page Lifecycle. In order to do more complex things in ASP.NET, such as creating dynamic controls and adding them to the web page at runtime, you MUST understand the page lifecycle.
With your issue, you must create that button every single time that page loads. In addition, you must create that button BEFORE events are fired on the page. Control events fire between Page_Load and Page_LoadComplete.
You want your controls loaded before ViewState information is parsed and added to controls, and before control events fire, so you need to handle the PreInit event and add your button at that point. Again, you must do this EVERY TIME the page is loaded.
One last note; page event handling is a bit odd in ASP.NET because the events are autowired up. Note the Load event handler is called Page_Load...