Cable modem question / equipment issues

Hi,

If power blinks, my cable modem needs a lot of manual hand-holding to come back up correctly. I'm wondering if it's an equipment problem on my end or something with my ISP.
My modem is an Ambit U10C018, router is a WRT-54GL running Tomato.
First, the router has to be unplugged while the modem boots or it doesn't pull an IP (via DHCP). I know this matches conventional instructions (plug in the modem, then plug in the router), but this is the first cable modem I've ever encountered where it actually matters.
Second, I can't simply power cycle the modem. I have to leave the modem unplugged for a solid two minutes or again it won't pull an IP. To me this seems like an awful long time for just residual data to clear from memory.
Can I fix likely fix this on my side by replacing my equipment - fixed defined as gear just boots and works - or is the lengthy power down a matter of waiting for something on the ISP side to notice the disconnection and reset?

Any help will be apprecited.

I didn't find the right solution from the Internet.

References:
https://arstechnica.com/civis/viewtopic.php?f=10&t=1148659
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Thank you.