I made well over the $600 threshold to receive a 1099-MISC from the company. I contacted the company and they stated that "We do not send tax forms to any publishers". I'm using Turbo Tax Business to file my taxes and I know how much I received from this company. Would I just enter the income as General Income? Why would this company choose not to issue tax forms? The income I received from this company is rather high, would the IRS think its unusual that I don't have a 1099-MISC?
I'm not sure how this gets entered in TurboTax, but this income from the company should be included in the Schedule C (or C-EZ) Line 1 Gross Receipts total, along with all of your 1099-MISC income from your business and any other income that your business took in. You don't need a 1099 from them, and the IRS doesn't care (at least from your perspective) if you got a 1099 or not; in fact, they probably expect you to have some non-1099 income.
We don't know why the company chose not to issue 1099 forms, but luckily it isn't your concern. You can fill out your tax return properly without it.
Note: This answer assumes that you didn't have any tax withheld from your checks from this company. If you did have tax withheld, you'll need to insist on a 1099 to show that.