Two Layovers
 

I am a U.S. citizen and live in South Korea.

I have an upcoming trip soon, and the trip is:

Seoul to Guangzhou, China, and a two hour layover.
Guangzhou to New Delhi.

Two weeks later:
New Delhi to Guangzhou for a two hour layover.
Guangzhou to Seoul.

My question is, am I allowed to have 2 layovers in China? Do I need a visa for a multiple entry? I have had major difficulty in the past trying to get in and out of China, and have had to miss a trip to Thailand because of it. Any advice would be great.

You have two separate transits. Each time going to a third country. Definitely fine.

You are now entitled to 72 hours visa-free layover at Guangzhou (and several other major cities) so long as you have an onward ticket, and may even leave the airport. Just changing planes isn't an issue. China works like everywhere else in the world (except the US) and understands the concept of transit.

China isn't like the rest of the world in terms of Intl-Intl transit. In China, PEK T3 at least, you still need to queue up for the "transit" immigration line, which can be longer than other lines.

CAN may be better.

China is hardly alone in requiring you to line up, be re-scanned, and present documentation before being allowed through transit. The same principles apply, and unlike the US you are not required to have a visa nor to enter and exit the country.

The US is the worst in the world, but China isn't exactly the same as most countries with airside Intl-Intl transit. To suggest or believe otherwise is foolish.

The foolishness is the pointless waffle and the waving around of the word 'foolish'. No one has said that China is 'exactly the same as most countries' but that like most other countries (those with significant air traffic, anyway) there is visa-free transit passage. Not unusually, lining-up and re-scanning is necessary when passing through. No answer already made to the OP is affected in the slightest.

'Am I allowed to have 2 layovers in China?'

Yes.

'Do I need a visa for a multiple entry.'

No. No visa at all is required.

You are fine visa-wise but two hours is "legal" but risky in my opinion.