It looks like you've got an EFI/UEFI-mode Ubuntu installation to a Master Boot Record (MBR) disk. This is unusual -- unusual enough that it may be causing problems. The usual configuration for an EFI-mode installation is to use the GUID Partition Table (GPT), not MBR.
With EFI-mode booting, the boot loader is stored as a file on the EFI System Partition (ESP; your /dev/sda4), and a reference to that file is stored in NVRAM. I've done very little testing with this, but some computers seem to "forget" that NVRAM entry when using MBR, and there's evidence that this is what's happening on your system -- if you search for efibootmgr in your Boot Repair output, you'll see that the critical ubuntu entry is missing from some of its runs, which implies that the ubuntu entry is not "taking."
If I'm right, then converting your partition table from MBR to GPT and re-running Boot Repair might fix the problem. This conversion is fairly simple and can be done with my gdisk tool, which comes standard with Ubuntu. See the gdisk documentation for details:
http://www.rodsbooks.com/gdisk/mbr2gpt.html
Note that this conversion, although quick, is not entirely risk-free. The risk is fairly low, but if something goes wrong, it will go badly wrong and could easily result in the loss of a lot of data. Thus, if you have important data on the disk, you should back it up before you do this conversion. (See below for another reason to perform such a backup.)
Unfortunately, some EFIs are buggy and can't remember their boot loader settings even on GPT disks. This was common in 2011-2013, but is less common on more recent computers. If your system is so afflicted, you'll need to implement a workaround, as covered in far too many questions and answers here:
One more point: Your /dev/sda2 is NTFS. It doesn't look this this partition is bootable. Using NTFS on an Ubuntu-only installation is inadvisable because there are no good NTFS maintenance tools for Ubuntu, which means that when (note: when, not if) the NTFS partition needs repair, you'll have to jump through tedious extra hoops to fix it. Thus, unless that partition is actually a bootable Windows installation, I strongly suggest that you back it up, convert it to a native Linux filesystem, and restore it. If it is a bootable Windows installation, converting the whole disk to GPT will render it unbootable, at least unless and until you install an EFI-mode Windows boot loader on the computer. Thus, if you're still booting Windows from this partition, you may want to go with a solution other than the MBR-to-GPT conversion I've suggested, such as installing a BIOS-mode boot loader for Ubuntu on the disk.
