I think the Austrian Theory of the Business Cycle (or perhaps more accurately, the "Credit Cycle") can help shed some light on how recession, banking and money can be connected.
Let's imagine a country with vast farmlands. A number of entrepreneurs open warehouses that offers 2 services. A farmer can deposit his excess grain for a small fee in case he wants it later. He gets a receipt stating how much grain he has deposited. This receipt can be traded for good and services. Other warehouses may collect it and demand that the specified amount of grain is transferred to them. Alternatively the farmer can authorize the warehouse to loan out, say, 1 ton of grain on the condition that the recipient will give 1.1 tons back at a later date.
"Fractional Reserve Banking"
Now let us imagine that one of the warehouses decides to pull a clever trick. If its customers have deposited 100 tons of grain, the warehouse could secretly take 50 tons and loan them out. The warehouse collects the storage fee and whatever interest they earn on the loan. As long as there aren't too many people showing up at the same time to withdraw grain, the trick will be a success.
The problem is that the "money supply" has now increased. The farmers have claims to 100 tons of grain, while the loan recipient has a claim to 50 tons (even though in reality, only 100 tons are available - not 150!). The farmers and the recipient will start projects under the faulty assumption that 150 tons of grain are available to pay construction crews, architects etc. These projects will be to numerous or too elaborate to be completed since there simply aren't enough real resources to go around.
At some point, individuals or other warehouses, that have obtained the duplicated receipts will start to demand the real grain from the first warehouse. Since they can't all be paid, work will seize and the half-finished projects will plummet in value. Whatever businesses were started to contribute to these projects must close and sold to the highest bidder. A recession has occurred!
To answer your question, you are correct that recession should not occur in a world with a fixed money supply. However, the process described above where deposits are turned into loans is perfectly legal and an integrated part of the modern banking world. Part of the reason is the belief that expanding the money supply stimulates growth (jobs are certainly created, but whether they are actually productive/sustainable can be debated). If one adds the ability of central banks to physically or electronically issue more fiat money, it is easy to see why the idealized , but understandable assumption underlying your question is not actually valid.
I can recommend the following link for a more detailed treatment: