How do I select long-lived microcontrollers for designs so we do not have to revamp our product if they stop making the chip?
Brand based answers are usually frowned on BUT Microchip with their PIC microcontrollers do a superb job of not obsoleting hardware products that are decades old. If you look in their catalog and selection guide pages you will find products that are not recommended for new designs but which they were making in the early years of their operation. Upgrade paths are also often relatively pain free compared to some alternatives. 

PIC processors have for decades had a very large % share of the bottom end market - in equipment like cable TV set top boxes, toys appliances and more. In Asia they are competitive against direct contenders. For high volume manufacturers I understand that they offer untested products at a significant discount, allowing suitably capable manufacturers to run their own acceptance programs.

For an entry level processor in high volume you will certainly be able to get standard PIC parts down to around $US0.20 and I imagine substantially below that - but I have no way of accessing such information as it would be on a 'need-to-buy' basis. 

Another approach is to look for generic processor families that are manufactured by a range of suppliers. eg Various 8051 variants 

Atmel are specifically not good at maintaining long product lifetimes. 



Update - January 2016: It has just been announced that Microchip has arranged to buy Atmel, so it will be interesting to see what changes this causes. These could range from discontinuation of some Atmel products, through to improvement of long term availability.