Yes it does.
Brimstone blast text reads as:
###BRIMSTONE BLAST
Lesser; 3rd; Eldritch Essence
This eldritch essence invocation allows you to change your eldritch blast into a brimstone blast. A brimstone blast deals fire damage. Any creature struck by a brimstone blast must succeed on a Reflex save or catch on fi re, taking 2d6 points of fire damage per round until it takes a full-round action to extinguish the flames or the duration expires. The fire damage persists for 1 round per five class levels you have. For example, a 15th-level warlock deals 2d6 points of fire damage for 3 rounds after the initial brimstone blast attack. A creature burning in this way never takes more than 2d6 points of fire damage in a round, even if it has been hit by more than one brimstone blast.
(emphasis mine)
Bonus damage from a source is applied only once in any case so it would be applied only on the cast of the eldritch blast and the critical hit would only apply to the attack roll of the eldritch blast, ongoing effects never critically strike unless specified because they require no attack roll to begin with. Also you can't stack another ongoing fire damage from a different brimstone blast due to the rules of Same Effects with different Strenghts, what would happen is that you would get the new duration of the following blasts in case the victim fails his reflex save again.
So to sum it up your damage would be xd6 from Eldritch blast+2d6[Mortal bane], this is the damage of your attack, and then 2d6 of fire damage every round because the target is on fire.
Also from Stacking rules we have:
Stacking
In most cases, modifiers to a given check or roll stack (combine for a cumulative effect) if they come from different sources and have different types (or no type at all), but do not stack if they have the same type or come from the same source (such as the same spell cast twice in succession). If the modifiers to a particular roll do not stack, only the best bonus and worst penalty applies. Dodge bonuses and circumstance bonuses however, do stack with one another unless otherwise specified.
This Means that if Mortalbane damage would apply to more than one instance it would be stacking with itself on the same effect, since like I stated previously everything is generated from the same single source.