Andy has some good suggestions and I'd like to add, if you're able to narrow down a particular contact whom you can email/snail mail/call about your AR, you're saving yourself a lot of time.
At the outset of the relationship ask them to set the expectation with you about how long it takes them to turn around and pay you and in what manner will the payment be sent. Take down that person's name, note the date/time if it's done through a phone call, save the email - you know the drill.
After your invoice is sent out factor in how many days it takes for the mail to physically get there, then factor the number of days to process the invoice (3 - 5 business days?). So maybe you're looking at a period of 15 business days before you should reasonably expect to get your payment. Set a reminder in your calendar to call or email them on business day 16. On day 16 call up ask to speak to your contact. Ask if he/she received your last invoice. If no, fax or email to him/her directly if that's an option... otherwise it's back to the post office. Ask them to contact you when the invoice is received, and ask again for when you can expect your payment to be sent out from them to you.
If you get the feeling that they're aging your AR intentionally (because it's consistently taken months to get paid on several invoices), get on the phone with someone senior in the AP department, or talk with your sales point of contact, or someone else with whom you have a relationship and who has authority in their organization. The key is to have this conversation with someone who has the power to do something about your situation.
Start off lightly, say that your accounting department is hassling you about the AP and you're following up to see if they need you to send another invoice, etc. The answer will be yes or no.
If yes, send it out and tell this person that you're going to send them directly because last time you sent it to their AP department it looks like it disappeared. Have them contact you when received. If they don't want to do that, tell them that for the last X amount of times you've sent the invoice into the AP department it's gotten lost or taken X amount of days to be paid. Let this person know at this time that the expectation was set with you by someone in their organization, that it would take X amount of days for your payment to be sent out. Use this conversation as a chance to figure out why that's not happening. First tell them that the aging is a monkey wrench in your organization's works and your accounting department tasked you with resolving it. Ask direct questions to your client. Please explain to me why my invoices are being aged for X amount of weeks? Is your financial situation not solid enough that your company is able to pay on time? If the answer to this is yes, then its time to start finding new accounts to fill in for this one.
If the senior member says no, they do not need you to send another invoice, then you have the opportunity to ask probing questions. Let them know that you sent your invoice 3 weeks ago and you haven't gotten a payment, and someone in their organization told you that the typical turnaround time is X number of business days. Again, let them know it's a monkey wrench for you and the accounting department is breathing down your neck about resolving it. Ask for their explanation on why it's taking so long.
You should have a series of fall-back positions ready if they are aging. Maybe you can stop selling to them. Maybe you can't. Figure out what options you have and what options you would like to hear from them. If it's a big problem for you, then it's a big problem for them. Be reasonable with them and tell them that you need their payment to be more timely or more consistent and that a lot of stress is being placed on your organization because of the aging. Work out a scenario that will allow you to get paid. Maybe it's a matter of having them pay partially over time. Would this be acceptable to you? The more info you have about what's going on inside their organization, the better you'll be able to determine your options.
Also, it's always a good idea to include a clause in your contracts about accruing interest on aged invoices over X amount of time.
These are all possible ideas of how to approach the situation. If they're intentionally aging your invoices you've got to do some detective work and use the soft skills to get what you want. When possible, make it look like your accounting department are the bad guys, and you're just delivering the message. If you're at the point when you have to consider stopping business with this client, tell them that, but let them subtly know it's because THEY are not paying you. You're the good guy in all this, and you just want to get paid.
Good luck.
