Is it really time?
Python, 45 43 38 27 bytes
For inputs up until 239999:
lambda n:n/100%100<60>n%100
You can try it online! Thanks @Jitse and @Scurpulose for saving me several bytes ;)
For inputs above 239999 go with 36 bytes:
lambda n:n/100%100<60>n%100<60>n/4e3
Perl 6, 33 25 bytes
-7 bytes thanks to Kevin Cruijssen
60>*.polymod(100,100).max
Try it online!
APL (Dyalog Extended), 19 bytesSBCS
-10 bytes thanks to Kevin Cruijssen.
Anonymous tacit prefix function. Takes argument as integer.
⍱59<100∘⊤
Try it online!
100∘⊤ convert To base-100
59< are they, each, greater than 59?
⍱ are none of them true?