Try connecting a 10 uF capacitor between the reset and ground pins on your Mega.
Perhaps during bootloading you set fuses to values that require an external crystal to be attached to the ATmega328p, but you don't have a crystal attached.
Are you trying to upload the next sketch using serial via the bootloader, or continuing to use the mega as ISP?
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OK I just wanted to make sure you weren't trying to use serial and the bootloader to upload, such as through an FTDI adapter or something like that. It would add an additional thing to troubleshoot. Plus whenever you upload a sketch such as the blink sketch via programmer, it removes the bootloader from the ATmega328p. That is OK, because when you're uploading a sketch with a programmer, you don't need the bootloader anyway. It is still good you did the burn bootloader step, because that is when your fuses are set. Anyway, it seems to me you may have an intermittent problem, which is annoying. Many things could be causing that. Bad wiring, something wrong with the soldering, power supply, circuit design, etc. It is probably time to show us a full schematic of your circuit or board, and perhaps a good clear photo of the board. Robin2 made this guide that you may find useful, to include displaying the picture in your post, instead of just plain upload that shows a link. https://forum.arduino.cc/index.php?topic=519037.0It is not mandatory, but it may increase the audience that will participate in trying to help you troubleshoot.