Acrobat Pro not scanning with HP OfficeJet Pro 9020e.

Acrobat cannot scan, at least not by itself. There is NO scanning function within Acrobat. Rather, Acrobat uses other software to scan. On a PC, this is done via a "linking" software called Twain. On the Mac, Twain has limited capabilities for the same reasons they kicked off Flash (too many potential virus issues). So, what they do instead is provide a TWAIN link to Apple's "Image Capture" only.

My guess is that the link-capabilities to the HP scanner are not as robust as those going to the Brother. I have no way to know where the fault lies, that being TWAIN or the HP scanner. Here, Acrobat is the middleman and can only be blamed for the issue.

I encourage you to scan with your scanner’s software, save your scans in the TIF format, and leave the files on your desktop (or wherever convenient). Then, you can drag the files onto the Acrobat icon in the Dock. If you save the files as TIF images, Acrobat will automatically OCR them; there's nothing else you have to do. If you drag more than one file onto the Acrobat icon, Acrobat will ask you if you want all of these files merged into one document or to remain separate.  (If you save in any other format, the auto OCR dynamic will not happen, and you'll need to add to your workload by adding an OCR step to your activities.)

Some extra tips and bits of information: A full-page, 300 ppi, 8-bit TIF file will be about 8 MB. (16-bit will be about 16 MB); once they are processed into a PDF, they will drop down to about 100-150 kb, so do not worry about the size. Assuming that you've done a pre-scan to set the Levels settings to get a clean image and you're doing a stack of pages from the same source, there's no need to do subsequent pre-scans. The first scan will be "document.tif." The 2nd document will be "document (2).tif," the third will be "document (3).tif," etc. When you process those in Acrobat, the first scanned page will end at the end of the PDF as the last page. You can either fix this in the "Organize Pages" or, before processing in Acrobat, change the name in the Finder or Explorer for "document.tif" to "document (1).tif." (There's no way around this because it is up to Finder or Explorer to name it, not the scanning software.

When I scan from my HP MFPs, I do so from the printer's panel, scanning to a network file. I rarely use the scanner interface from my computer. 

Try scanning to a JPEG file or TIFF file using the scanners interface without scaning from Acrobat.