Over his career, Nathan had been a stellar pitcher. Since he was moved to the bullpen by the Giants in 2003, he has pitched at least 64 games and over 64 IP in ten of the last eleven seasons. Other than undergoing Tommy John surgery in 2010, He has stayed remarkably healthy and consistent. Outside of 2011, his last year with the Twins, he has produced AT LEAST 1.2 WAR per year over that span. That is nearly unheard of. Over the last 25 years, there are only 3 pitchers that have produced more WAR as a reliever than Joe Nathan (20 WAR). Those three players are Trevor Hoffman (23.0 WAR), Billy Wagner (23.6 WAR), and Mariano Rivera (39.8 WAR).
I looked back over his career splits, and it does appear to be true. His worst performances are typically in March/April. In March/April, he has posted the worst K/9 rate (8.78, next worst month is 10.30, career average as RP is 10.60), BB/9 (3.15, next worse is 3.13, career average as RP is 2.73), BA against (.222, next worst month is .213, career average as RP is .186) WHIP (1.19, next worst month is 1.05, career average as RP is 0.98), FIP (3.38, next worst month is 2.88, career average as RP is 2.70), xFIP (4.04, next worst month is 3.23, career average as RP is 3.16) and OPS against (0.655, next worst month is 6.02, career average as RP is 0.551).
Some of the struggles seem to leak over into May, as his "next worst" BA against, WHIP, and OPS against are all in May. In addition, he has posted his highest HR/FB% rate in the month of May (10.2%, career average as RP is 7.2%).
This was all especially true in that aberrational 2011 season after returning from TJ surgery. April of that year was arguably his worst as a MLB pitcher. In 9 IP, he had an ERA of 10.00, K/9 of 7, BB/9 of 7, 1.78 WHIP, 0.929 OPS against, and a 7.03 FIP. This terrible stretch lost him the closer job, which he wouldn't get back until mid-July, and may have impacted why he didn't resign with the Twins (although money was probably a big issue in that smaller market, especially as the Twins were entering a "rebuilding" phase). I understand that this one month may be an outlier skewing his career April numbers, but that's just not the case. His season to season splits show similar, albeit smaller, blips in April and occasionally into May.
In addition, we can chart his fastball velocity over time the last two seasons. Although there is a slight decrease in his overall fastball velocity from 2012 to 2013, he generally picks up a few MPH as the season goes on. That said, his fastball velocities from this year do not look encouraging, but hopefully those will also increase.
Ultimately, I hope Joe Nathan knows what he's doing and is able to bounce back. I did look at some of his top player comparisons on his baseball reference page and seeing the names of Todd Jones and Troy Percival on there is a tad bit frightening.