Are Bitcoins destined to forever increase in value?
In theory yes. If demand grows at a steady rate this will certainly be the case, as less coins will be produced making what is available more desirable.

In reality there are other factors which could affect the value of bitcoins.


Alternate chain could supersede bitcoins (unlikely at this time)
Vulnerabilities like what has appeared (with hacking) already in the main markets
Overspeculation of market trends


Think of it more like gold than a fiat currency in the likelihood of behaviour (nb. my opinion, may not be the case)

If the value does keep increasing it can split into eight decimal places to make a very large number of potential units of currency.