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Not an answer, just illustrations from some quick simulations. Immediately below, the previous position of the walker is blocked with probability $\frac{1}{2}$, and blocked for just one time step:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_1.jpg
Below, again blocked with probability $\frac{1}{2}$, but now blocked for two time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_2.jpg
And now three time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_3.jpg
Of course, in this model, it is quite possible to get "stuck," if the barriers last long enough (4 or more time steps in my simulation).

Not an answer, just illustrations from some quick simulations. Immediately below, the previous position of the walker is blocked with probability $\frac{1}{2}$, and blocked for just one time step:
         
Below, again blocked with probability $\frac{1}{2}$, but now blocked for two time steps:
         
And now three time steps:
         
Of course, in this model, it is quite possible to get "stuck," if the barriers last long enough (4 or more time steps in my simulation).

Not an answer, just illustrations from some quick simulations. Immediately below, the previous position of the walker is blocked with probability $\frac{1}{2}$, and blocked for just one time step:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100.jpg
Below, again blocked with probability $\frac{1}{2}$, but now blocked for two time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_2.jpg
And now three time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_3.jpg
Of course, in this model, it is quite possible to get "stuck," if the barriers last long enough (5 or moretime steps in my simulation).

Not an answer, just illustrations from some quick simulations. Immediately below, the previous position of the walker is blocked with probability $\frac{1}{2}$, and blocked for just one time step:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_1.jpg
Below, again blocked with probability $\frac{1}{2}$, but now blocked for two time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_2.jpg
And now three time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_3.jpg
Of course, in this model, it is quite possible to get "stuck," if the barriers last long enough (4 or more time steps in my simulation).

Not an answer, just illustrations from some quick simulations. Immediately below, the previous position of the walker is blocked with probability $\frac{1}{2}$, and blocked for just one time step:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100.jpg
Below, again blocked with probability $\frac{1}{2}$, but now blocked for two time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_2.jpg
And now three time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_3.jpg

Not an answer, just illustrations from some quick simulations. Immediately below, the previous position of the walker is blocked with probability $\frac{1}{2}$, and blocked for just one time step:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100.jpg
Below, again blocked with probability $\frac{1}{2}$, but now blocked for two time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_2.jpg
And now three time steps:
         Walk Barrier 100 steps http://cs.smith.edu/%7Eorourke/MathOverflow/WalkBarrier100_3.jpg
Of course, in this model, it is quite possible to get "stuck," if the barriers last long enough (5 or moretime steps in my simulation).