Do I need two transit visas for round-trip travel through the US?

After much digging, I found out that the number of entries a C-1 visa can be issued for is country-specific, based on visa reciprocity.

To find whether you can get a multiple entry C-1 visa (or any other visa type) requires consulting the US visa reciprocity tables, which tell you:

For temporary visitors (nonimmigrants) to the United States, the reciprocity tables available from the drop-down menu above show applicable visa issuance fees by country and by visa classification type, and the maximum period of visa validity and number of applications, or entries, that may be authorized.

For India, we see that a C-1 visa can be issued for multiple entries and a 60-month (five year) validity period. And to show that they do vary by country, see the tables for Iran, which show that only a single entry visa good for 3 months can be issued.

And as I've noted before, you can transit on a B-1/B-2 visa, so if you have any thought of engaging in tourism in the US at some point in the future, you may wish to apply for that visa instead. The cost is the same and it is good for 10 years.

It is indeed very hard to find whether the C-1 can be used multiple times but this document suggests that at least such visas exist. On the other hand, here is a C Visa which I think shows a 2 under the number of entries although it is somewhat hard to see but it's definitely neither 1 nor M. This makes me think that the C Visa can be 1, 2, M. I would apply once showing the need for two entries.

A US Visas official page says

A visa issued for multiple entries (denoted under “entries” with a certain number (2, 3, etc.) or “M” for multiple/unlimited entries)

So such a visa in general exists.

You can get B-1/B-2 visa if you wish to make multiple entries into the United States of America. That should be all you need. You can apply two at the same time.