Basically your definition and how it fits into your ideology.
The first thing I would say is that there is no single "middle class". That's a sociological rather than a social category- and although that's not to say that sociological class is irrelevant, because status groups, consumption groups, etc. do have a certain reality insofar as people believe in them, it's not even a particular useful category for sociological analysis. Instead, there are two social strata that you could call "middle class", although one of them isn't really in the middle, and the other one isn't really a class. So, um, bear with me.
First, you've got what Marx called the "petty bourgeoisie", which basically means small businessmen and other petty proprietors such as self-employed professionals, small farmers, and so on. While they own their means of production, they also work it themselves, and so the division between capital and labour does not appear, and they effectively sit outside of the capitalist class structure. Their status as a "middle" class is based on consumption, i.e. their socioeconomic status, rather than on their role in production.
Secondly, you've got a class which Marx himself never really addressed, but which is the main concern for later theorists of a middle class, and that's the "managerial" or "coordinator" class. As the name implies, this is a stratum comprised of managerial and administrative personnel, who, while separated from the capitalists class because they do not own capital (or at least not a socially significant amount of it) and must work for a living, are separated from the workers because their function is the oversight and management of production, rather than production itself. As such, they form a "middle" in the structure of capitalist production between the working "bottom" and the capitalist "top". (Trade union bureaucrats fulfil a similar role, although because they are mediating between labour and capital, rather than directing one on the half of the other, it's a little more complicated.) However, this intermediate position between labour and capital means that this class can't organised on an independent basis, which, as I said in my reply to Quackers, is that Marx is really interested in. In a certain sense, they are a section of labour, because they are waged employees like everyone else, but their role in the process of production is as an appendage of capital, so they're not in a position to independently oppose it. (You can't have "manager's self-management", if you see what I mean.) They might form a "class-in-themselves", in Marx's terms, but they are incapable of forming a "class-for-themselves", which is Marx's measure of a "true" class. Political organisation, for them, comes through attachment to other classes, almost invariably to the capitalist class (individuals may depart from this pattern, but rarely on a significant scale), or in certain periods of instability by attaching themselves to a non-class "Bonapartism", such as the interwar fascist movements or the anti-colonial nationalist (and "communist") movements in the third world.
[Edit: In retrospect, that last bit was over-simplistic. It's more true to say that the managerial stratum is capable of mobilising in pursuit of sectional interests within a given form of social organisation, but are not capable of mobilising in pursuit of a reorganisation of society in a different form. The two shouldn't be conflated as I do above.]
This brings up the question of what role these classes can have in any communist movement. As a class, they cannot have any role, because the working class, as Marx went to great pains to make clear, is the sole agent of its own emancipation. But as individuals? Well, that's trickier, and in all honesty I'm not sure where I stand in that. I don't see any reason to prevent someone apparently sincere in their beliefs from participating in left-wing politics, but I also think that it's necessary to maintain working class hegemony in the movement, or you'll just end up with something like the SWP which is dominated by academics and trade union officials. My provisional solution would be to allow "non-voting membership" to such individuals, with the extension of full membership on a case-by-case basis. But, I place only a limited emphasis on communist organisations (which I see as more properly concerning themselves with agitation and education than with pursuing "leadership"), so that's not as vital an issue for me as it might be for the various Trotskyist sects and what have you.
And I'm sorry that this was such a long post, but that's what happens when you ask commies about class.
