Is a self-sustaining "loop" of economy a thing?
This is not a "sustainable loop" -you neglect the concept of value-added, created by the use of additional factors of production in each company. 

Company $A$ has revenues $p_AQ_A$, with which it must cover all its expenses (including returns to capital).

These are only part of the costs of company $B$, because it also uses additional capital and labor to build the gearing system. So the revenues of company $B$, that have to cover expenses in order for $B$ to keep going, and given that it has purchased $Q_A$ units from $A$, is $p_BQ_B &gt; p_AQ_A$.  

These in turn, represent only part of the costs of company $C$. With the same reasoning, we end up with $p_CQ_C &gt; p_BQ_B &gt;p_AQ_A$. Not that the number of machines build by $C$ are the number of machines that $A$ demands in order to produce $Q_A$.

Under the described loop, company $A$ must now pay $p_CQ_C$ in order to do its job (plus any other costs for the labor and any additional capital it may be needed). But since $p_CQ_C &gt; p_AQ_A$, this will mean that company $A$ will have losses, even before paying for the other factors of production it needs to hire. Hence, the loop is not sustainable.  

A possible (misguided) objection ¨


  "But $p_CQ_C$ represents an investment for company $A$, it is not
  an operating expense"


Essentially this objection implicitly assumes that with $Q_C$ machines in hand, company $A$ will be able to produce more than $Q_A$ product units. But if this is the case, then after the first purchase, company $A$ won't demand more machines from $C$, hence $C$ won't demand additional gearing systems from $B$, hence $B$ won't demand any additional product units from $A$, and so any remaining productive capacity of the $Q_C$ machines will not be used. 
If this objection does not assume the existence of this additional capacity, then the $Q_C$ machines will fully depreciate in order to produce $Q_A$ product units -and then, there may be initially classified as "investment", but at the end of the production cycle of $A$ they will be recorded as "depreciation charge", i.e. a bona fide running expense (which is what they are, since they fully depreciate).

I would suggest to study Input-Output models of an economy.