Follow-up when promised a call in 30 days

Any reason not to follow-up when I was told that they like me, I am a top (possibly only candidate), but they decided to put the process on hold for 30 days?

A CEO of a local growing co. reached out to me on LinkedIn about a not-yet posted new tech support manager role. A face to face interview went very well. I followed MT follow up protocol with a hand-written thank you to all 3 interviewers. When I placed the phone call to the hiring manager he apologized for not getting back to me sooner, but half the office including the CEO had been out with the flu. He said he would email me soon which he did, saying they really liked me, had one small concern that may not even turn out to be an issue, but they decided to put their energy into hiring new techs and put the whole decison about me on hold for 30 days. I replied with appropriate statements of understanding, good luck with the search and stay healthy etc. That was early March.

And now I'm stuck and a bit nervous about whether I should maybe send a brief email along the lines of the advice in the radio silence podcast, that my job search is continuing and I'm still interested and I hope the hiring process is going well - asking no questions or making any demands. He told me it was on hold and promised to get back to me in 30 days - should I just leave them alone? I don't want to call, that seems rude. I am probably over thinking this but it's a small company and I don't want to appear insensitive or mistrusting of his promise to get back to me when they are ready. I could wait the 30 days, and just make sure not to jokingly say "your 30 days are up", but I'm thinking that maybe I should wait 30+? days. I hate this part of the process. Advice appreciated. Jeanne