Do the LEDs both light and stay on? Buy a lottery ticket, you are very lucky. :lol:
Is your battery dead?
Are you using blue LEDs that need 3.5V but your battery is only 3V? Use a 6V battery.
Are the wires on the LEDs the correct way around?
Are the pins on the transistors the correct way around?
Are the wires on the capacitors the correct way around?
Are the wires from the battery .......

Hee, hee. Stupid sim program!
Change one of the 10k resistors to about 9k then the stupid sim might come into the real world.

The simple multivibrator ain't rocket science.
One of the capacitors is going to charge quicker than the other due to small differences in the 10k resistors' or the 100uF capacitors' values.
Say R3 charges C2 quicker than the other side. Then Q1 turns on lighting its LED and its collector turns off Q2 through C1.
Then C1 charges a little in reverse by ...

Are you using tantalum capacitors???
Use electrolytics and your flasher will work fine. :lol:

The drawing board would be to answer the rest of my questions about the circuit. You'll spot what is wrong.
The power supply must be applied abruptly to these multivibrators. If the supply voltage slowly ramps up, then both transistors get stuck on.

You need to set an initial condition to upset the symmetry. Set the initial voltage on one of the bases to zero volts. I don't know how you do that with Livewire, but I'll bet it is possible. In SwitcherCAD III, you set a .IC condition.
AG's suggestion of using a PWL battery should also work. As he said, turn it on with a fast risetime.
You should also add a 2k resistor from each collector to +V, so the collector voltage will get all the way up to +V. As Audioguru said, you may not get much current through the LEDs, depending on what color they are.

Originally Posted by Ron H

You should also add a 2k resistor from each collector to +V, so the collector voltage will get all the way up to +V.

That will do the trick. Without these resistors, since the supply voltage is nearly equal to the LEDs voltages, then the capacitors hardly have a difference in current to make the circuit oscillate.

Unless the LED's are the low current type they only have about 3mA thru them, as the voltage across the LED is approximately 2V if they are
red, green, or yellow, about 0.2 volts Vce on the transistor so about .8 volts for the 330 ohm resistor, hence 0.8/330= .0024A or 2.4mA.
If it were my circuit I would change the 330 ohm resistors to about 75 ohms.

My 3V and 6V Ultra-bright Chaser projects operate their LEDs briefly at 25mA. I have (had) all colours.
My "Flashlights" (blinking torches) operate their ultra-bright LED briefly at a whopping 90mA like a strobe-light. I have (had) all colours.
My multi-coloured Fading Mood Llights reach a peak current in their LEDs of 30mA. They make millions of colours.
My Sound Level Indicator project beams its 20 red LEDs at 26mA.
Even my Plants Watering Watcher-2 projects blink their red LED briefly at 20mA when the plant is really thirsty and wilted (don't tell my wifey).

I have very bright LEDs all over my place! Only 2.4mA is dim. :lol: