At the present time, there are far more tenants looking for homes to rent than there are available homes. Simple supply and demand is dictating the terms of leases.
When the owner puts a property on the market for rent, they usually receive several applications. Then, it's up to the agent and the owner to discuss the pluses and minuses of each applicant.
Credit is usually the most important consideration. If you have poor credit, there is a reason. Maybe there has been one unfortunate event. Otherwise, it's because the income doesn't match the expenses. So, bills are paid late and lines of credit are extended and paid back with minimum payments.
It's a matter of risk. If the property owner will accept a tenant with poor credit in this market, they are looking for something to mitigate that risk. If a tenant with good credit will pay the equivalent of one month's rent as security deposit, then someone with bad credit carries a much higher risk. I've seen owners ask for as much as three months security deposit, along with 1st month's rent.
Ultimately, it's up to the individual property owner. There is no "standard". However, if an owner is asking for 3 months security, then I would ask why the owner doesn't have a better pool of tenants to choose from. I would wonder whether the owner was very honest, was him/herself distressed or whether the property iself was subpar.
I realize that someone struggling (and poor credit is generally an indicator) doesn't have thousands of dollars in reserve to give someone as a deposit...which isn't even going toward rent.
My advice is to stay where you are, improve your FICO score and take a look at it again in a year when you may have more options.
If you have to move when your current lease expires, you've got a tough road ahead. As I said, the demand exceeds the supply. The good properties can have multiple applicants who would all qualify to purchase homes. For an owner, that's an easy decision. If your credit is bad, deal with that upfront. There are fees to run credit reports. Don't waste everyone's time, including your own by failing to mention this critical piece of information. If the owner will look at someone with damaged credit, then proceed. But, don't think anyone isn't going to know you have a poor credit score. They will and no one likes surprises. It will affect your ability to rent that property in nearly 100% of cases.
I wish I could be more help, but I can't tell you that the prospects are good when they just simply aren't.