Yes, given that the opponent helps the capturing side, it is possible to capture en passant two times or more in a row.
Here's an example from a real game. Click on the arrows to view the game moves in forwards and backwards play. I have typed in a command to show the moment just before the two captures occur, specifically just before Black does the first relevant double pawn step.
The game can also be found here on chessgames.com.
[Title "Sergey Gennadyevich Kudrin-Rudy C Douven, GMA Baleares op (1989.12.??),Palma de Mallorca ESP"]
1.e4 c6 2.d4 d5 3.Nc3 dxe4 4.Nxe4 Bf5 5.Ng3 Bg6 6.h4 h6 7.Nf3 Nd7 8.h5 Bh7 9.Bd3 Bxd3 10.Qxd3 e6 11.Bf4 Qa5+ 12.Bd2 Qc7 13.O-O-O Ngf6 14.Ne4 O-O-O 15.g3 Nxe4 16.Qxe4 Nf6 17.Qe2 Bd6 18.Ne5 c5 19.Rh4 Bxe5 20.dxe5 Nd7 21.Rg4 Rhg8 22.Re1 Qc6 23.Qe4 Nb8 24.Rf4 Rd7 25.Qh7 Rgd8 26.Ba5 b6 27.Bc3 Qd5 28.b3 b5 29.Kb1 b4 30.Bb2 f5 31.exf6 g5 32.hxg6 Rxh7 33.gxh7 e5 34.Rxe5 Qf7 35.Re7 Qf8 36.f7 Qxe7 37.f8=Q Rxf8 38.Rxf8+ Qxf8 39.h8=Q Qxh8 40.Bxh8 h5 41.Kc1 Kd7 42.Kd2 Ke6 43.Ke3 Kf5 44.f3 Nd7 45.Kd3 Nb6 46.Bg7 a5 47.Bf8 Nd7 48.Bd6 Ke6 49.Bc7 Kd5 50.c4 bxc3 51.Kxc3 1-0
As an extreme showcase, here is a checkmate in seven problem that features 5 en passant captures in a row!
[Title "Милошески, Бошко Mihajloski, Zlatko, Novi temi 1975 Comm, Checkmate In 7 Moves With White To Move"]
[FEN "3r4/1pBpppp1/7n/PBk1PPPP/3R1K2/2rpP3/5NPn/8 w - - 0 1"]
1. Ba4 b5 2. axb6 d5 3. exd6 e5+ 4. fxe6 f5 5. gxf6 g5+ 6. hxg6 Rf8 7. Ne4# *
UPDATE: On the website Yet Another Chess Problem Database I found this problem that, amazingly, features the possible maximum of 7 consecutive en passant captures in a directmate problem. Stockfish solves in just seconds.
[Title "Велимировић, Милан, Novi Temi 1979, 1sr Prize"]
[FEN "r7/pppppppN/8/1PPPPPPP/1n5k/R5N1/3n2K1/8 w KQkq - 0 1"]
1. Ra4 a5 2. bxa6 b5 3. cxb6 c5 4. dxc6 d5 5. exd6 e5 6. fxe6 f5 7. gxf6 g5 8. hxg6 Ne4 9. Rxb4 Kg4 10. Rxe4#
EDIT: Thanks for so many upvotes everyone! I never expected this! This is now my most upvoted answer ever!