What happened to the overall click volume since you reduced the bids? Did impression shares change for any terms? (That would be my first suspect.)
Are you still top or second on exactly the same queries as before? Or has something shifted in the queries you're appearing for? If impression shares changed more for some terms than others, that could affect the balance of what you're appearing for.
Is the competition doing anything different? For example, it can affect your CTR if a competitor comes up with a more appealing description.
Finally, do you have tracking in place so you know which terms your enquiries are most likely to come from?
If you reduce your budget Google will reduce the amount of times that your ad is shown in order for your budget to last through your ad schedule. You may be #1 or #2 just for less auctions.
To build on the impressions thoughts above, outside of keywords it could also be time of day, region, or device. Are you getting less visits during high converting hours, regions, or devices?
Also it could be seasonality or even placebo (just a dry spell that is unrelated to the reduces spend). I also do a lot of PPC and over the last month certain time periods have felt off which doesn't surprise me as Google has had quite a few bugs lately.
"so I cut back the bids on our largest spenders."
Cut back bids on the least efficient converters instead.
Find and cut wasted spend, I guarantee you can find lots.
Feed the winners, starve the losers!
For special promotions we can track who we win as business easily but more day to day stuff can come in via phone calls, emails, contact form (rarely), web chat, and the like - and it is hard to tell who came from which traffic source, and whether as a result of SEO or PPC.