IPhone – Internet Sharing: Using the MacBook Pro as a Wifi Modem with its Ethernet Connection for the iPhone, connectivity issues

1. Do you have DHCP enabled? Your laptop might be loosing its connection to the router due to IP conflicts resulting from other devices on your network using the same IP address.
2. Try using different broadcast channels. I think the default Linksys channel is 6. I usually use 8 or 1.
3. How good is the signal strength? You might have to boost the antennas transmission signal.
4. Make sure someone like your neighbors are not running APs with the same SSID.
5. If you use signal encryption try using different key encryption WPA/WPA2-PSK(AES/TKIP).
6. and the obvious one, run software updates, just to make sure that there is no new firmware for the MacBook NIC.

Your Macbook is bridging 2 different networks.

The first, from your router, would presumably be 192.168.1.0
That would make the router itself 192.168.1.1 & it will then hand out DHCP addresses from 192.168.1.2 up to as high as .254

In order to prevent potential IP Address conflicts. Apple's Internet Sharing will use an address of one order higher for each Ethernet connection you ask it to use [with Thunderbolt or USB adapters, this could be many, on rare occasions] so the first one will be 192.168.2.x, the one after 192.168.3.x etc

The only thing that puzzles me slightly is that the reported self-assigned address is 169.254.x.x. This is a private, self-assigned address that an interface will use if it cannot find a DHCP server to assign it one.
For a bridged connection, though, I would have expected it to assign itself 192.168.2.1, as the gateway for your bridge & not be trying to pick up a DHCP address at all, as it is the 'router & gateway' to your new node.

The fact that your second machine can connect successfully with an assigned address of 192.168.2.2 & a gateway of 192.168.2.1 would tell me that the self-assigned address might be misreported somewhere along the line; as otherwise it oughtn't to be able to connect.

After some extensive Googling I discovered this, which may explain the apparent discrepancy.

If you toggle your Internet Sharing on and off, you'll see the bridge0: device appear and disappear from ifconfig. This makes things tricky depending on the static IP you assigned your Pi as well as your Mac. If you chose to use DCHP for your Mac Ethernet connection, your Pi will only work with a static IP that looks like 169.254.x.x; however, when you turn on Internet Sharing, your Pi will then only work with an IP that looks like 192.168.2.x. It turns out that if you used DHCP for your Ethernet connection and your Ethernet has an IP of 169.254.x.x AND you have Internet Sharing on, you can still connect to your Pi via a 192.168.2.x address since now the bridge0: device is the one handing out the IP address to connected devices.

TL:DR
Don't set DHCP on your shared connection in the Macbook, because it is supposed to be the 'master'. Allow the OS to set it up itself, which it will do correctly, with a fixed IP of 192.168.2.1 for itself & 192.168.2.2 ..3 ..4 etc for devices using it as a bridge