There's a huge difference between a dead and a "struggling" (or "dying") civ.
Dead civ:
- Two migrant waves (at most, can be reduced by necro sieges and pop caps).
- Never any dwarven caravans
- Never any monarch
- The only known certain indication of whether a civ is dead or "merely struggling" is that the civ screen' civ screen is completely empty upon embark. Normally you have your parent civ and your site government there. Once you get into contact with another civ (via caravan or attacks) your (dead) civ and site government is added to the screen.
- Logic does not apply to whether civs are dead according to DF, due to a very buggy process. Civs can have had no members and no sites for thousands of years without being considered truly dead.
- Dead civs can't raid, at all, presumably because it's the civ that performs "army" movements, and dead civs do nothing. Note that sending off messengers is the same as "raiding" from this perspective, so if a messenger returns the civ isn't dead.
There are a number of legitimate reasons for the caravan not arriving, as well as a number of buggy ones.
Significant loss of dorfs in one factor scaring away migrants, and trade is an important attraction factor, but fortress worth should be an attraction factor, so you might try to produce expensive stuff and build it in the fortress (I think weapon trap components are valuable, for instance).
If you have visitors, you can recruit new fortress members from petitioning visitors, but avoid performance troupe petitions, as they're bugged (and I suspect they're bugged to a fatal crashing level). It takes two years for them to petition for citizenship, but at that time they're full citizens and can be ordered around as normal (avoid mercs, as they never petition for citizenship, and squads of mercs have to be led by a citizen. Monster slayers will never petition for citizenship [as far as I know: I don't know if any has survived for two years]).
As far as I understand, you can only request migrants from sites economically liked to your site that are also a member of your civ, so if that site belongs to another civ you can't request anyone.
You can, as mentioned, also aim for a dorf breeding program. It should be a fair bit easier now than it was earlier because of the relaxed age difference restrictions, but you may still have trouble getting two breeding pairs out of your 6 dorfs, given that some won't marry and some don't have any hetero sexual orientation component, and, on top of that, some have personality traits that indicate they're going to be rather difficult to get married ("finds the concept of marriage to be utterly repulsive", is one clear example). It ought to be possible to get dorflets out of Lover relationships now, though (I haven't seen anyone reporting it happening in a fortress, though).
Given that you've got to deal with two or at most 3 pairs, setting up nuptial encouragement suites shouldn't be too hard, and once married, regular (i.e. yearly, or so) procreation encouragement sessions can be organized using similar techniques.