I don't think it's a correct analysis at all. I'll address each point:
"The Liberal Democrats will "disappear into the annals of history" unless they pull out of the coalition"
Utter Bull.
If they pull out of the coalition now, all they will prove is that they are unwilling (and therefore unfit) to govern when the economy is not doing well. There is nothing more certain to make a party disappear into the annals of history than refusing to govern when the opportunity arises.
The fact is (despite what many people are saying) is that the LibDems are having quite a lot of say in how the country is run. They ARE having to back policies that they opposed before the election - but that's being done in order that they can get policies of their own through that the tories were opposed to.
* Those on low incomes are benefitting from the income tax cut - an extra £200 per person might not sound like much to some, but for those of us on low incomes it's a much needed boost that would never have happened without the LibDems in government. The tories (and labour, for that matter) opposed raising the tax threshold. The tories have backed a LibDem policy they opposed.
* Local enterprise partnerships - another LibDem policy that's already benefitted many places - not least the regeneration of Redcar with the reopening of the steelworks. 6 months from now - the steelworks in Redcar will be producing high quality steel. 23 other similar projects have been funded throughout the country in the 1st wave of investment. The second wave of investment is just beginning. The tories would have made investment easier wherever it was most profitable (ie - investment concentrated in the South East) - whilst labour were always going to decide that at Westminster rather than give local communities control. A Lib Dem policy (opposed by the other 2 parties) is regenerating areas of the UK.
There's a lot more - but this site has a word limit. This link may be of use:
http://www.whatthehellhavethelibdemsdone.com/
"or will the British be more forgiving and give the lib-dems a reason to stay with the Tories by voting yes to the Av vote."
Whatever the result of the referendum, the LibDems will not implode over just one policy. Whether or not the coalition lasts does not depend upon the result of this referendum.
This is a choice between keeping the current system or moving to AV. Whatever your opinion of the LibDems - the chance to make MPs more accountable to the electorate is worth taking.