Whilst you say it'll be dropped after the third season, the first season of Dr Who managed best-of-day ratings for every time an episode was first shown in the UK. It takes either majorly spiralling production costs - or massive audience declines - for a show to go from that to cancelled in another 2 seasons.
Quite simply, I do not think it will decline that quickly.
As with the 'old' Dr Who, I suspect that the production crew will begin changing every few years as well - I cannot imagine RTD keeping at it forever, nor can I imagine him being allowed to keep the job if he cannot continue to deliver good ratings.
The BBC invested a lot of money in this, and so will not be willing to let it die off so soon. If the staff begin to underperform, ratings-wise, then they will be replaced. The same counts towards the actors, of course - underperform, and be written out.
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