Theories about how lack of supply can feed into lack of demand

A simple way to do this is to "qualify" the utility effect of the good by an index of "ease of access". Denote this index $e(X^s)$, that we assume depends on the market supply of the good $X^s$,

$$0 leq e(X^s)leq 1,;;;partial e/ partial X^s >0.$$

Assume one good and "all the rest" $x$ and $y$ respectively. Assume a quasi-linear utility function of the form

$$U(x,y) = y + u(e(x^s)cdot x),;;; u' >0, u''<0$$

$$s.t,;;; y + p_xcdot x = I.$$

So if the consumer buys $1$ unit of good $x$, its utility effect corresponds to the utility effect of a lower quantity, if ease-of-access is not perfect ($e=1$). Solving the utility maximization problem, one gets (the value of the Langrange multiplier at the optimum is here equal to unity due to quasi-linearity),

$$e(X^s)cdot u'(e(X^s)cdot x) = p_x.$$

For a concrete example, assume that $u(z) = 2sqrt{z}$. Then the first-order condition becomes,

$$ frac{sqrt{e(X^s)}}{sqrt{x}} = p_x implies (x_d)^* = frac {e(X^s)}{p_x^2}$$

At the optimum, demand depends positively on the "ease of access" index, which in turns depends positively on total market supply. If the latter goes down, $e(X^s)$ will also go down, and demand of the individual will go down.

At market level, with $m$ identical consumers, market clearing requires

$$X^d = X^s implies mcdot frac {e(X^s)}{p_x^2} = X^s,$$

which is an implicit equation in $X^s$.

Lack of supply of a network good - a good associated with a network effect - may result in lack of demand for that good. The greater the number of people who have or use such a good, the greater its value to any one person. Hence a lack of supply of such a good to some people will probably reduce demand from those to whom it is available. For example, if there were a temporary lack of supply of phone use in city A (eg due to technical connectivity problems) making it impossible for people to make or receive calls, then demand for phone use in other cities might be expected to reduce by the amount of calls that would normally have been made to or from city A. More fundamentally, some goods with the potential to create network effects may never be supplied and used in sufficient quantity to establish such effects, so that demand for them remains minimal (even though it might, if supply had been large enough and other circumstances such as first-mover advantage had been favourable, have become very large).

Possibly not what you had in mind, but if X and Y are complementary goods, then lack of supply of X can result in lack of demand for Y. For example, a shortage of pasta might result in reduced demand for pasta sauces. Or closure of sports centres (eg due to Covid-19) might reduce demand for sports clothing.