The first trace shows the ADS board working, the second smaller trace when it does not work correctly.
You can see that the arduino is sending the SCL and the ADS is returning a signal. So, I assume that the board is working and does not require replacement.
I am not using a 4k7 pullup resistor, not a 10k. I ran out, but this does not seem to be affecting the signal.
The arduino now only seems to be sending a single byte (8-ish) of SCL signals, and not the 50+ it did before.
Everything you see in the second picture is by the Arduino. There is no one else on the bus.
At the begin and end is a START and STOP condition.
Between that are 9 clock pulses (a high level of SCL).
The first 7 pulses is to put the I2C address on the I2C bus. The Arduino is using the SDA for the I2C address. The 8th clock pulse is the R/W bit.
The 9th clock pulse is where the ADS1110 should pull the SDA low for a ACK. But it doesn't do that.
When the Arduino does not get a ACK after the I2C address, then it assumes that it is not there. The Arduino does not send data anymore, only the STOP condition.
Run a I2C Scanner sketch. Try to make it work by checking all the wires. The ADS1110 might be broken.
I have checked the soldering/wiring and it is still not working. I have ran a I2C bus scanner, and it is not showing the ADS1110 at address 0x48, so I think it might be broken.
I will report back when the replacement arrives and is fitted.