I agree price will not stabilize, and that generally speaking, it is on an upward trend. However due to a large number of influences on price, while moving upward it will periodically find valleys.
Oil will probably stabilize somewhere in the 60-80 range, and then depending on the particular influences acting on it at the time, either shoot higher or come back down. Most governments have an interest to keep oil from shooting off the charts, so they will do everything they can to keep it below a certain point, whether that means subsidies, increased drilling/production, limits on consumption, etc; regardless of the shortsightedness of their actions.
Reality check:
These are the projections for oil production in the next 40 years based on Hubert Peak Oil theory:
today: 27 billion barrels a year
2020 - 20 billion barrels a year
2030 - 13 billion barrels a year
2040 - 9 billion barrels a year
2050 - 5 billion barrels a year
How elastic do you think the demand for oil is? It is a very good moment to ask this question given what is happening right as we speak in Europe where countries are declaring nationwide emergency just after one day of disrupted gas deliveries.
So, given that supplies will be steadily decreasing, at what point do we hit the inelastic demand level, below which we can't go and at which point prices will really sky-rocket?
Nobody know for sure, but it is highly unlikely that is is below 20 billion barrels a year now, much less that it will be below 20 billion barrels a year in 2020 when we have another 2 billion mouths to feed
P.S. Also, we should not forget that the price is not determined by supply and demand only, the perceptions of the market have an enormous influence. Right now most people still haven't waken up to the reality of Peak Oil, the real disaster will come when this happens