Describe more. Not visible on what screen? Are they not visible before you import and visible after the import is done, or something else? Does "not visible" mean there is a grey rectangle where the photo should be, or that there is no rectangle at all for certain photos, or something else? If possible, show us a screen capture.
Also, please state what version of Lightroom you are using and what your operating system is.
When I select Import, the only photos that appear are through 2011. Of 9,000+ photos on my MAC, only 3,300 appear as able to download to LightRoom. Trial Lightroom subscription (2015). MAC OS X Yosemite 10.10.3
Are you saying that the folders that contain images after 2011 don't appear in the import dialog box?
Are you saying that when you go to folders that contain images after 2011, that the photos don't appear? Or do they appear but you cannot import them?
Or, are all the photos in a single folder and only the ones 2011 and earlier show in the Lightroom import dialog box?
What does "appear as able to download to LightRoom" mean? Exactly how does Lightroom show you that the photos "appear as able to download to LightRoom"? What do you see on your screen?
I really think a screen capture would help at this time. If that's not possible, we need you to describe this in HUGE AMOUNTS OF DETAIL, not a single sentence.
The actual pictures taken after 2011 appear on my MAC in the Photos App. They do not appear when I select Import in the LightRoom app. As such, there is no way to select them to import to LightRoom. A screen shot in LightRoom app just shows the photos available to import and those photos do not include any images taken after 2011.
Did you change cameras around 2011? What camera took these missing photos? What version of Lightroom do you have installed? Are the missing photos RAW or JPG or something else?