This is the race to the bottom. It is unsustainable for good quality work. Delivery value, quality, results, then you'll spiral up not down.

Rule number 1 - don't discount
Rule number 2 - even when you have to discount, don't

If for a good strategic reason you absolutely have to drop the poverall price, don't discount, but offer a once off element of the service for free.  That keeps your price point in the market and the client recognises the "freebie" is a once only offer.
 

Lot's of businesses do it, especially big ones. If you are going to do it, know that it will cost you, do the metrics on it and consider using it to draw people in to see other things at full price.

The only way to avoid discounting spiral is by not going that rabbit hole.
Don't even start, as there will be NO end to that, and these customers just shout TROUBLE!
I would never agree to that, as it is  disrespectful to the work I do, the caring, time, effort I put into my work.  

Never, research your market and I choose to use a mid-range hourly charge rate.

Position yourself as the expert.  High quality, excellence in all you do.  Show the value you bring and what is being provided for the price you charge.  Realise that people will pay for excellence.  If you get into the 'sharpen the pencil' game you will always end up in a downward spiral.  If the client really sees value they will pay.  If they don't see value try harder to show that or go to clients who understand what they are paying for.

It's an age old question - to discount or not to discount?  Great discussion. Thanks for contributing @Michael Simonetti @Keith Dugdale @Steve Gray @Orna Binder @Greg Reiffel @Malcolm Dawes