GE heavy duty digital timer model 15440: unable to change day if week unless I enter incorrect date or year. Doing so interferes with auto adjustment for daylight savings time and leap years. Unable to program individual days of week when the timer doesn't know what day it is. It thinks today is Thursday when it is Monday.

I agree 100% with RAY. You can get one for 12 UsD at Amazon

GE Indoor 7 Day SunSmart Digital Timer

I do not recognize that timer model number.
The only place the model number appears is on link to fixya... indicating that the model number does not correspond to known product, or that some seller has renamed a timer so his product cannot be comparison-shopped.
Re-post question and attach photo

Most GE manuals appear on following link: open link to find same-similar timer
http://waterheatertimer.org/GE-timers-and-manuals.html

Gene
Water Heater Timers Save Money

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

1) Copy following link to identify timer and download manual:
http://waterheatertimer.org/GE-timers-and-manuals.html

2) Add comment and describe timer in detail for further assistance

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

I cannot repair defective timers, and there are complaints about this timer's MODE button.
Most people complain they can't get mode to set.
Avoid the MODE button after programming timer.
Reset the timer by pushing CLOCK PROG MODE buttons. Then re-program the timer per instructions, and then press CLOCK button to exit programming and timer is in Auto mode and ready to work.
No need to press MODE after programming timer.
Typically, this timer has limited 1 year warranty.

http://waterheatertimer.org/pdf/GE-15117-Manual.pdf
http://waterheatertimer.org/GE-timers-and-manuals.html#15117
15117 is not heavy duty timer. Both outlets combined are rated 1000 watts incandescent and 1/4 HP. Check nameplate on your pump for HP rating.

For limited-lifetime-warranty timer, rated 1/3 HP, choose Intermatic HB800RCL 2-outlet timer.
Cost twice as much as GE 15117.
For 1HP outdoor pumps choose Intermatic P1121
http://waterheatertimer.org/Intermatic-timers-and-manuals.html

Most digital timers suggest resetting as last-step effort to restore functionality.
This particular timer is reset by removing battery.
Try removing battery again. Otherwise it seems the timer has gone bad.
HB88RC is discontinued product.
Replacement is heavy-duty Intermatic HB800RCL 2-outlet or HB800RCH 1-outlet timer.
http://www.smarthome.com/25078/Intermatic-HB800RCL-Heavy-Duty-Digital-Appliance-Timer/p.aspx
http://www.smarthome.com/48715/Intermatic-HB800RCH-Outdoor-Digital-Timer/p.aspx

Less expensive and less reliable timer Woods 59403 with 1-outlet has quite a few 'timer won't work' questions on fixya.
http://www.amazon.com/Woods-59403-Heavy-Duty-Outdoor-Digital/dp/B002KS7EOK
http://waterheatertimer.org/Woods-timers-and-manuals.html#6-24

Hi
Please copy and paste.
Regards

http://waterheatertimer.org/pdf/GE-15042-15079-15089.pdf

EI600 is a heavy duty 20Amp in-wall timer that is battery operated, and can replace single-pole or 3-way switches.
Intermatic page
http://www.intermatic.com/products/timers/in-wall%20timers/electronic%207-day%20astro%20time%20switches.aspx


EI600 manual
http://www.intermatic.com/~/media/files/intermatic/products/instructions/timers/ei600c%20-%20english.ashx

DZS400 product descriptor shows DST, and many other programming options:
1) This might help or not:
You can modify DST start & end times > Press MODE until dSt shows > Press MONTH, DATE, DAY to modify start times, and then press ENTER. (or press DEL and ENTER to delete) > Press MONTH, DAY, DATE to modify end times, and the press ENTER > press MODE to return to AUTO.

2) According to DZS400 product descriptor "The controller has 365 day holiday capabilities with 24 single dates" ... if above solution doesn't work, the 24 single dates might provide enough days to fill in programming gaps in the DST. Your manual should have programming steps.

To program the ST01C:
http://waterheatertimer.org/ST01C-program.html

ST01C manual:
http://waterheatertimer.org/Intermatic-st01c.pdf

1) Manual has troubleshooting. Since ST01C is battery operated, it will not work on loads farther than 100 feet away from timer. If a wire is buried underground, this can interfere with operation. Other electrical devices can interfere with timer operation.

2) Solution:
a) Check for interference issues listed above.
b) Press MODE and make sure it is set to AUTO. If timer will not enter AUTO then no program has been set.
c) Re-check your programming as shown in step 6 of manual. Remember timer offers 40 programs. To set Program 1 >> 'on' time has to be entered and saved for Program 1 >>> and then 'off' time has to be entered and saved for Program 1. And then press MODE and set to AUTO.

To change the time on a prostar 816 you first need to be at a display set (doesn't matter what the extension number is).
with the handset down, enter #20 the screen should say MMC DISABLED
1) enter in 1 2 3 4 1 # (that enables programming)
2) enter in #55 the screen should say YYMMDDWHHMM
3) enter in the year, month, day, day of the week, hours and minutes(the day of the week values are 1= mon. 2= tues. etc.)
press # when finished.