The original specification was one sample per 8 seconds. You need to charge the capacitor faster to support that sample rate.
I see. I missed that and yes you do need to charge the cap faster to meet the 8s sample rate.
The easiest thing to do would be to decrease the resistor. At that point, however, you're risking however your PC chose to interpet section 18.104.22.168.1 of the USB spec:
22.214.171.124.1 Over-current Protection
The host and all self-powered hubs must implement over-current protection for safety reasons, and the hub must
have a way to detect the over-current condition and report it to the USB software. Should the aggregate current
drawn by a gang of downstream facing ports exceed a preset value, the over-current protection circuit removes
or reduces power from all affected downstream facing ports. The over-current condition is reported through the
hub to Host Controller, as described in Section 11.12.5. The preset value cannot exceed 5.0 A and must be
sufficiently above the maximum allowable port current such that transient currents (e.g., during power up or
dynamic attach or reconfiguration) do not trip the over-current protector. If an over-current condition occurs on
any port, subsequent operation of the USB is not guaranteed, and once the condition is removed, it may be
necessary to reinitialize the bus as would be done upon power-up. The over-current limiting mechanism must be
resettable without user mechanical intervention. Polymeric PTCs and solid-state switches are examples of
methods, which can be used for over-current limiting.
Generally speaking, voltage sources only have two ways to deal with overcurrent: shutdown or foldback (aka removes or reduces power), and neither of them are particularly good for VBUS. PCs seem to do anything from shutting down the port temporarily to shutting down the port until reboot to current limiting at 100mA even if it takes 30s for the bulk cap to become charged. It is almost certain, however, that you could decrease the resistor to the point where the cap is recharged after 8s yet your particular PC is still happy.
More complex methods of limiting inrush current to a bulk cap are possible, however, the simplest of which would be two resistors and a FET.