Every economics text book which I have seen shows a simplified circular flow diagram similar to this:
It shows the transfer of money between different groups in the economy over a fixed period of time. For valid simplification, it ignores the government and foreign sectors at first.
Savings is shown as a leakage from the circular flow, and investment as an injection. Books conclude that preventing contraction of the economy requires private investment to equal savings. For example, "Macroeconomics in Context" by Goodwin et al. contrasts the classical theory of the market for loanable funds, where interest rates equalise savings and investment, with the Keynesian model in which this may not succeed (and therefore a depression can result unless the government supplements aggregate demand).
It seems to me that the model needs some very careful thought before conclusions are drawn.
When I think of the circular flow of money in the economy now, it is much closer to this diagram:
For simplicity, it does not show interest payments, and also ignores firms' savings with banks. Those features could be added, but I believe they would be distracting here.
By showing more leakages and injections, this diagram helps to avoid what I now consider the artificial attempt to make investment (the only injection in the original diagram) equal savings (the only leakage). For equilibrium, withdrawals plus lending should equal savings plus repayments. The diagram also challenges the implication that, for example, new savings will exceed withdrawal of previous savings in any particular time period.
Since the purpose of savings is to be able to spend today's earnings later, and since banks insist on being repaid, no market for loanable funds — or government action — is necessary in order to equalise the injections and leakages, at least not in the medium-to-long term, because each of the red arrows generates a debt, obliging the recipient to transfer the same amount of money in the opposite direction (the adjacent light blue arrow) in future. Each leakage and injection is ultimately reversed.
What I believe this shows is that Say's Law is in fact correct over the long term.