Bed bugs can lay eggs for a maximum of 13 days without a blood meal. Thereafter the bugs can not lay eggs. When a bed bug egg hatches, the new hatchling is highly vulnerable to desiccation and will die within 5.68 days to 26.3 days depending on humidity (Usinger page 14). Therefore if we continue catching bed bugs after 39 days (usually it is much less) after treatment we know the bugs are continuing to feed and lay eggs after treatment. If a tenant cooperates with bed isolation and laundry protocols it is very rare for us to continue catching first instars in the bed leg traps. If the tenant fails in bed isolation and laundry protocols it is normal to continue catching first instars. Therefore the presence or absence of first instars in bed leg traps after a couple weeks make a good indicator for tenant cooperation.
Update July 10, 2014
Missing from the above calculation of the maximum time for first instars to be present is the time required for hatching of the egg. This varies depending on temperature or even on the variation of temperature (Usinger) so I allow about a week for average centrally heated homes.
In practical terms we always retreat / inspect at two weeks. The first two weeks always have first first instars present in the traps. The second inspection (at 4 weeks) often has some first instars but sometimes there are zero. If I find first instars at the six week mark I start wondering about what is going wrong but I accept that it is theoretically possible for first instars to still be present. If bugs are present at 8 weeks I know something is amiss.