Phone LED only flashes for a few minutes after receiving a notification
Must be by design. Flashing the LED infinitely would drain the battery (even if only slightly). I don't see anything in Settings regarding lengthening the amount of time the LED will flash; you can only specify what things cause LED notification.

After some searching it looks like the "Missed Reminder" app allows for a lot of notification customization - LED interval, color, etc. Not sure how to link an app so just search for it in the market. Sounds promising. Hope it helps.