Why doesn't capitalism run out of money?
First of all there are several incorrect statements in your text: 


Investing money is not just raking in the cash. It involves a risk, actually non trivial part of the reason why you earn interest on money you invest is the compensation for you taking this risk. If you consistently take bad risks you eventually lose your money, so its not correct to say investing is just like "rake in the cash". Moreover, if you invest in your own business/projects you have to put entrepreneurial work in. The only portion of the return that you could consider as "raking in cash" is the portion that you get to compensate you for opportunity cost of not investing the cash but enjoying it.
There is no economic theory that says in capitalism lives should get worse. In fact in economics we dont even use term capitalism - but assuming you mean by capitalism mixed but predominantly market based economies there are no economic theories which says life should get worse in those. Note in science we usually use theory differently from common English. A theory must be some consistent and testable explanation of some mechanism, and often we reserve the word theory only to consistent explanations that were already successfully tested and supported by evidence.
Money in economy circulates. Unless the rich investor stuffs the money under a mattress, it is incorrect to compare her or him to vacuum cleaner. If you put your money in bank it will get lend out to people who need it. If you spend your money on high living then again the money is paid to producers of the stuff you enjoy. 
You cannot invest any number of money you want and expect the same return. Ultimately you will experience diminishing marginal returns on your investment. As the supply of savings increases interest rate goes down as in a present situation when in some countries interest rate is even negative, so you get punished by saving and rewarded by borrowing money. 


Now to answer your main question, why the economy does not run out of money (assuming no more printing of new money), it is because prices in economy adjust. Generally, the monetary part of macroeconomic can be described by classical monetarist equation which states that:

$$MV=PY$$

Where M is the money supply, V velocity of money, P price level (change in which will give you inflation/deflation), and Y is the real output - how much goods and services economy can produce. 

Now lets assume that money supply is fixed (hence no more printing of additional money), and examine the effect of investment on this relation. First, real output actually depends on level of investment. The higher level of investment, the higher number of factories and capital workers can work with so also the higher output we get. So investment increases the real output Y. Real output is also actually what determines the well being of people within a country (at least as measured by lets say GDP per capita). However, to keep the equation balanced something else has to change. One possibility would be for velocity of money to increase- i.e. the speed in which money circulate, but velocity of money usually does not change much. So most likely what will actually happen will be that aggregate prices P decrease, meaning that for the same amount of money you will be able to buy more goods and services. 

Lets also for a second suppose that rich would actually stuff all their money in the mattress and never used them in any way possible. This would just be equivalent of actually decreasing money supply M and again P or V would adjust. In the short run decline in money supply could also negatively affect Y, but in the long run output Y is fully determined by the production capabilities of economy not by number of dollar bills circulating. 

So in either case sustained increase in material welfare is possible. Also, note redistribution is not actually about taking the money from rich and give them to poor its ultimately about transferring the resources from one to another. So redistribution also does not actually necessarily depend on availability of money in the economy (although thats a topic of its own that I wont go into).

So to sum it up, some of the premises in your question are not correct, and the answer why you can have a sustained increase in wellfare when money stock declines is that prices (or potentially also partially velocity) adjust. The total output and hence material welfare of country is (in the long run) independent on quantity of money.