Technology has changed for the better.
Batteries going weaker has no effect, since they use voltage regulators that maintain the voltage exactly at a specific level, until the input voltage drops below acceptable levels. Sort of like digital TV compared to analog. It either works right or not at all.
These also use the displays readout to show you current status as % of charge, so you know all the time how they are doing. You also never need to change them if you don't want to (comes with 4 AA 2400 NiMH rechargables). While still using the unit, simply plug in the cig lighter plug into your power port for 30 minutes when power drops as low as you care to chance it, and good for another 6 to 20 hours. (sorry, again forget how long they last as it has not gone low on my short trips the past few months).
This has saved my butt a few times. Don't know about reduced range, as it has worked better on batteries than any direct wired detector I have ever used in 35 years of driving. Has warned me of radar more than a mile ahead.
google search found this model reviewed at RadarTest had these comments:
http://www.radartest.com/article.asp?articleid=10055
Best under $200 cordless unit. 4 out of 5 stars.
Rates excellent range.
They show tested range of over 5 miles.
The only cordless model to operate without a reduced duty cycle, with payoff of improved performance.
EDIT: I did use Dual Lock, not Velcro. This has 4 AA batteries, so it is a little large and heavy. Perhaps it will hold better on a dash shelf than on the master cylinder.