Can I leave Canada while my PR application is being processed, and is there a 30 day limit?

There is no thirty-day limit in the guide itself. If you are applying under the Provincial Nominee Class, the IRCC application guide for that class, last updated 14 September 2026, says nothing about travelling while your application is processed and sets no limit on how long you can be outside Canada.
If someone has given you a number, ask them where it came from. The likeliest honest answer is that it is their own rule of thumb. The other possible answer is that it sits in your nomination conditions, and if that is where it lives then it is real and it binds you, so read what your province actually required of you.
What does carry risk on a trip has very little to do with how long you are gone.
Your status has to stay valid, and entry is assessed every single time you arrive. A pending PR application does not entitle you to come back in.
If you hold an employer specific work permit, your authority to be in Canada runs through working for that named employer. A long absence is not a problem if your employer has approved the leave and the job continues. It becomes a different conversation if the absence effectively ends the employment, and that is a question about your contract rather than about immigration.
And the one people actually get caught by. Requests arrive with deadlines attached, biometrics and medical exams especially. Being out of the country when one lands is the most common way a trip genuinely costs you time. Have someone watching your portal and your email while you are away.
Note that guides differ by programme. Some other IRCC guides do carry explicit wording that re-entry cannot be guaranteed if you leave during processing, so read the guide for your own application rather than someone else's.
Source: IRCC, Guide P7000, Application for Permanent Residence, Provincial Nominee Class, canada.ca, updated 14 September 2026.
This is general information rather than legal advice, and it reflects the guide as it stood on the date above.