Linksys router w/SMC modem/AP: Losing Connection!

[smithch]

My network is set up as follows

ISP -- SMC modem/access point -- Linksys wireless router -- PC (Win XP)

My problem is that the PC connection is lost intermitently and
frequently. I suspect an addressing issue because executing

>ipconfig/release
>ipconfig/renew

at the command line always restores connectivity immediately.

Here is the LAN description provided on the SMC modem/accesspoint
administrative page:

IP address
10.1.10.1

Private Address pool
From 10.1.10.10
To 10.1.10.199

PPTP IP Address pool
From 10.1.10.200
To 10.1.10.229

Here is the LAN description provided on the Linksys router's admin
page:

local IP address
192.168.1.1

Start IP address
192.168.1.100

Number of addresses 50

DHCP Address range:
192.168.1.100 - 192.168.1.149

DHCP server is enabled on both SMC device and Linksys device, and both
devices are using subnet mask 255.255.255.0.

My thought is that the loss of connectivity arises as a result of an
addressing conflict which occurs when the SMC device's DHCP server
attempts to assign an IP to either the PC or the Linksys device.

Honestly, I don't even know if theses two machines should be connected,
given that the network part of thier IP's are 192 and 10, respectively.

I investigated the possibility of putting the SMC modem/access point
into bridge mode, but I don't see that that's an option.

Any suggestions on what you think might be causing the loss of
connection and/or how I might fix it? Thanks!

smithch