Hi Kendra,
I had a hard time getting in to the industry too! I spent six months submitting resumes to over 200 local property management companies before one finally gave me a chance. I started at the bottom of the bottom. No pay, just comp rent in a tiny complex in a terrible neighborhood. So I worked my way up in the company by volunteering for special projects and committees, covering other personnel at other properties for their vacation time, and really getting to know all the ins and outs.
If you haven't already done this, try revising your resume so it sounds like all the work experience you already have is directly transferable to the position you want. Need customer service experience? A part time job at Starbucks will give you that. Filing experience? Volunteer at the library. Policy and procedure? Become a notary. Landlord tenant law? Volunteer for your local renters rights organization. Tech savvyness? Get your ham radio license. (I actually did ALL of these things, so I can attest that this works!)
Another thing you can do is be in the industry even if you aren't currently working in it. Go to the trade shows, job fairs, landlord forums, etc. Be outgoing and friendly there, network and make connections.
I hope you will love a long, successful career in property management!