WiFi: iPhone 3G does not always connect

I have Wi-Fi at home from the BT Home Hub that creates my broadband connection to my computer. I have set the Wi-Fi settings of my 'phone to connect automatically to my BT Wi-Fi, but occasionally this does not happen and I have to go to Settings>Wi Fi and tap on the name of the Wi-Fi network. This then immediately makes the connection, so it does not seem to be a temporary fault in the Wi-Fi provision itself that causes the automatic connection to fail.

This is a matter of some moment because if I fail to notice that the 'phone is not connected to Wi-Fi, anything I do on the 'phone drains the money in my pay-as-you-go mobile 'phone account. I should be grateful for any suggestions.

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