For medium size aircraft, yes. For over 100 or so seats. 3 years is around about right. However, it is not a disaster if you don't buy new aircraft.
For large aircraft (over 200 or so), you will pay quite a bit in maintenance either way, but 3 years is probably the limit.
For smaller aircraft, you can keep them longer, as maintenance is not as high.
Another thing you may want to consider is their resale value. At 3 years or so, many airlines will still buy them at their value or a little discount. By 5 years old, few people (excluding start up airlines) would touch them without heavy discounting. With smaller aircraft, even after 3 years, the demand for them is often decreasing anyway.