Personally, I think that the key term here is "overwhelming odds", this suggests that the paladin knows that he will not survive the battle if he stays. Given this, we have to look at the situation from the two perspectives of the paladin's alignment: Lawful(ness), and good(ness).
Goodness: This is probably the simplest issue to address, will more good be achieved through staying and dying, or from running away? The issue with this question, however, is that it is the paladin who is making this decision. He must firstly ensure that concerns for his own wellbeing are not overshadowing the larger cause. Secondly, if he has been told to stay, then he must ask himself if he is able to make as informed a decision as his superior is. Does he know all of the facts? Is he as wise as the person who gave him the order? After taking these into account, he must decide whether is is better (from a good perspective) to stay or leave.
Lawfullness: This is a much more difficult situation, as often laws are not entirely clear, or contradict each other. An example where killing one innocent will stop the world exploding (no, there isn't any other way to stop it happening) illustrates the point. In a situation such as this the paladin must ask himself which law takes precedence, "don't kill", or "stop people dying". In the similar situation of the bridge (where the extra few second s will make no difference) the question is "obey orders" vs "stop people dying"/"help the cause".
Even if the paladin can come up with reasonable answers to both of the above sections, there are countless situations where the two will be in conflict. In these situations I believe that it is unduly harsh to penalise the paladin for making either decision, as no answer was "right".
There is another area that the paladin must also consider, that of his own importance. He should be able to put modesty aside and think just how valuable his own exstence is. The situation would be very different if the paladin were on the verge of retirement as opposed to if he were the only person who could close the portal allowing the demonic hoardes to attack his homeland.
Given all of the above concerns, I do not think that it is possible to give a definitive answer as to whether it is OK to run away from overwhelming odds. Each situation must be assessed on its merits. Of course, one could ask why the DM would ever put the PC in a situation where the only choice was death or acting in an unpaladin like manner, as such lose/lose scenarios aren't fun for anyone.