It's well known that if you put carbonic acid $\ce{H2CO3}$ into water it will dehydrate into carbon dioxide $\ce{CO2}$ and water $\ce{H2O}$. Indeed this is how modern fizzy drinks generate their fizz. Taking this as a given what I don't understand is why doesn't sodium bicarbonate dissolved in water not slowly give off $\ce{CO2}$ via the following pathway:
$$ \ce{HCO3- +H+ <=> H2CO3} $$ $$ \ce{H2CO3 -> H2O + CO2} $$
This would lead to the solution of sodium bicarbonate slowly converting itself into a solution of sodium hydroxide. The first part of the reaction is reversible and is something that at equilibrium will have a non-zero amount of $\ce{H2CO3}$. In fact given that carbonic acid is a weak acid there will be a lot of $\ce{H2CO3}$ present at equilibrium. I also can't see how the presence of sodium ions in solution would inhibit the second reaction (since that is the only difference between this solution and a solution of pure carbonic acid which does effervesce) so according to my understanding we should be seeing a fizz .
However very clearly this bubbling does not happen in real life, as anyone can easily verify for themselves. So what inhibits it then?